The striker scored the opener before a second deflected off Alan Hutton for an own goal after the break as the champions recorded only their third win of the season
Diego Costa's tap-in and an Alan Hutton own goal gave Chelsea their first win in four matches on Saturday as the Premier League champions beat Aston Villa 2-0 at Stamford Bridge.
Both sides came into the clash out of form and separated by just four points in the lower reaches of the table but Costa - returning from a suspension for his antics against Arsenal last month - proved key as goals in each half got Jose Mourinho's men back on track after a tricky run of results.
Mourinho was charged by the Football Association in midweek for his outburst after the 3-1 defeat to Southampton and dropped the likes of Eden Hazard, Gary Cahill and Oscar to the bench from that loss.
While the changes made little difference early on as Villa edged the opening stages, Costa benefited from a defensive mix-up between Brad Guzan and Joleon Lescott 10 minutes before half time.
Villa - winless in the league since the opening day - offered signs that they could get back into the game but were out of luck for Chelsea's second as Costa's shot looped past Guzan off the unlucky Hutton.
While Chelsea continued to look off their best, Mourinho's side ended their winless run ahead of a tricky midweek trip to face Dinamo Kiev in the Champions League, while Villa's fifth consecutive Premier League defeat will keep the pressure on Tim Sherwood as they remain in the bottom three.
Carles Gil was one of four Villa changes and the Spaniard fired over from distance five minutes in before Ruben Loftus-Cheek had a curled effort deflected wide at the other end.
Villa again threatened as Hutton outmuscled Premier League debutant Baba Rahman before firing at Asmir Begovic - his follow-up effort veering way off target as Sherwood's men sought to ask questions of their hosts.
Jack Grealish - another brought in by Sherwood - posed problems, winning a free-kick on the edge of area that Jordan Ayew clipped just over as sloppy touches in the final third continued to plague Chelsea.
Villa continued to spurn chances - Rudy Gestede poking over the crossbar from inside the area - before dismal defending from Guzan and Lescott gave Chelsea their first clear opportunity.
The Villa goalkeeper took the risky option of playing it out to Lescott and, when the defender failed to control, Willian collected the ball and played in Costa for his third goal of the season in all competitions.
Grealish and Gil offered Villa their best chance of a leveller before half time, with Grealish cutting in from the left and going close early in the second half.
Mourinho introduced Nemanja Matic for Loftus-Cheek at the break and, while Chelsea struggled for attacking momentum, a fortuitous deflection off Hutton doubled the hosts' lead.
Costa took down Cesc Fabregas' lofted pass before turning and shooting on goal - the deflection off Hutton proving vital in beating a helpless Guzan and all but take the game away from Sherwood's side.
Lescott almost made amends for his role in the opener but was denied by Cesar Azpilicueta after Gil's dangerous delivery before Costa was back in the thick of things when he tangled with Ashley Westwood off the ball.
Both went unpunished by referee Roger East as Villa endured a frustrating defeat despite matching their opponents in spells.
The Blues defeated Aston Villa 2-0 at Stamford Bridge on Saturday as they returned to victorious form, and the Portuguese hopes for an uplift against the Ukrainian champions
Jose Mourinho has urged Chelsea to take confidence from returning to winning ways when they face Ukrainian champions Dynamo Kiev in the Champions League on Tuesday.
A Group G defeat to Porto had contributed to a three-match winless run for Mourinho's side amid a rocky start to the campaign before Saturday's much-needed if unconvincing 2-0 Premier League victory over Aston Villa.
Mourinho opted to bench a host of regulars as Diego Costa's opener and an Alan Hutton own-goal gave the hosts maximum points at Stamford Bridge ahead of their trip to Ukraine.
The Chelsea boss visited the Olympic Stadium in Kiev earlier this week for Ukraine's defeat to Spain on a reported scouting mission - speculation suggesting he was watching Kiev attacker Andriy Yarmolenko - and Mourinho has hinted he could bring back the likes of Eden Hazard, Oscar and Gary Cahill to add stability.
"I asked the players to look at the picture in a different way to a normal situation," he said of Saturday's selection.
"To look at a picture where I have to try to make decisions to bring results back, and when the results are back and we have better stability in our confidence levels, then go back to what you are.
"We were able to find these ingredients that we need especially when we are not playing at a top level.
"When you are not playing at a top level and on top of that you have no concentration, you make defensive mistakes, you don't defend well, you lose the ball and you don't have 10 players fighting to recover it as soon as possible, you cannot win.
"So let's try to keep this mentality, let's try to keep this tactical attitude and at the same time with a little bit more happiness and confidence, go in the direction of what we are."
Victory over Maccabi Tel Aviv on matchday one means Chelsea are third in the group, a point behind leaders Kiev, who have also beaten the Israeli side and drawn with Porto.
Sergey Rebrov's men go into the game off the back of a 3-0 defeat at the hands of title rivals Shakhtar Donetsk, but were boosted by a new five-year deal for star man Yarmolenko in the build-up to the loss.
The loss was Kiev's first in the league since April 2014 and former Tottenham striker Rebrov has called for a reaction from his side.
"I want to apologise to our supporters. We are all upset," he said.
"Still we must forget this terrible match and start getting ready for the game against Chelsea. Nothing horrible has happened in the Premier League for us.
"We have the same number of points as Shakhtar."
Portuguese believes he and his squad have the talent to build on the result after a shaky start Jose Mourinho believes Chelsea have "a very good manager and very good players", but has warned that victory over Aston Villa does not make them the Premier League's best team again.
Saturday's 2-0 win at Stamford Bridge - which came courtesy of a Diego Costa strike and an Alan Hutton own goal - was only the champions' third from nine Premier League matches in 2015-16.
Mourinho was keen to stress afterwards that the vital three points do not solve everything, but spoke of his confidence in himself and his squad to build on the result.
"We were not three years ago the worst team in the country and now we are not the best team in the country," he told BBC Sport.
"We are just a team with a very good manager with very good players trying to reach our normal level.
"But it is not because of one victory that we become great again."
Chelsea are 10 points behind Premier League leaders Manchester City and the Portuguese boss was reluctant to be drawn on whether he thought a charge for the title was definitely out of the question.
"I don't know," said Mourinho. "I just know that Tuesday we have a game [at Dynamo Kiev in the Champions League] and I think we can win it and next Saturday we play against a fantastic team with a manager [Slaven Bilic] who is showing all his qualities at West Ham but we still think we can win.
"We will go like this, match after match and see what can happen."
However, Mourinho was unimpressed when asked why Chelsea could only manage three shots on target throughout the victory over Tim Sherwood's men.
He said: "You always try to find negative things, even when we win.
"I don't want to go in that direction. I just want to say that we won and we deserved it."
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