Eden Hazard slotted home a sweeping early move from the visitors before Jores Okore headed in shortly after half-time to score Aston Villa’s first Premier League goal in nearly 11 hours, but Ivanovic’s thunderbolt sealed the points for the visitors.
Oscar had been denied by Brad Guzan while Willian went close with two low efforts in a scrappy affair, but Ivanovic’s goal was enough for Jose Mourinho pick up his first win at Villa Park in six attempts.
Chelsea, who have now gone four games unbeaten, move seven points clear at the top of the table after Manchester City were held by Hull.
The visitors dominated the early possession and were in front after eight minutes when Oscar moved down the line and found Willian, who slid an excellent pass into the box for Hazard to stroke across goal and into the far corner.
Villa improved after that and started to see more of the ball. Fabian Delph looked to play an instrumental role and set up a good chance for Agbonlahor, who could only head the midfielder’s cross off target.
Chelsea had a good chance to double their lead soon after as Ramires caught out Tom Cleverley before Nemanja Matic found Oscar with a good through ball and the Brazilian’s near-post effort was superbly turned away by Brad Guzan.
Mourinho’s men allowed the visitors more possession in what turned into a scrappy affair, but they had another excellent chance as Hazard spotted the run of Ramires, who collected his pass and moved into the box only to be denied by a stunning last-ditch challenge from Ciaran Clark.
But Villa raced out of the blocks after the break and, after Andi Weimann’s volley and Tom Cleverley’s deflected shot both missed the target, the hosts’ goal drought was finally broken three minutes into the second half.
The hugely impressive Carles Gil showed some good footwork to give himself some space to cross from the right, and Okore rose unmarked at the far post to nod it past Courtois for Villa’s first Premier League goal in nearly 11 hours.
The visitors were rattled but soon found their composure, and Willian almost put Chelsea back in front, firing two efforts just wide of Guzan’s post from distance.
But Mourinho’s men retook the lead on 66 minutes as Cesar Azpilicueta raced down the left and charged into the box. His low cross was blocked by Okore but he managed to play it to the far side of the area, where Ivanovic met it with a superb left-footed volley which flew into the top corner.
The Blues have shown some excellent game-management skills in the past and Mourinho used them to full effect once again, introducing John Obi Mikel to the fray as Chelsea saw the remainder of the game out with little incident to move seven points clear and tighten their grip on the Premier League title.
Phil Thompson’s verdict
“Chelsea played the better stuff – they always looked in control but it wasn’t them at their sharpest. It was not a great day at the office, but they do enough. He knows how to win games, Jose Mourinho.
“Villa did OK. They gave themselves a good chance in this game but it just wasn’t good enough. They’ve got the monkey off their back. They’ve done it – OK it wasn’t a striker who scored, it was a centre-back – but they’ve done alright.”
Aston Villa: Guzan (7), Hutton (7), Okore (7), Clark (8), Cissokho (7), Cleverley (5), Westwood (7), Delph (7), Weimann (6), Agbonlahor (5), Gil (8).
Used subs: Cole (6), Benteke (6), Sinclair (6).
Chelsea: Courtois (6), Ivanovic (8), Terry (6), Cahill (7), Azpilicueta (8), Ramires (6), Matic (7), Willian (7), Oscar (6), Hazard (7), Drogba (5).
Used subs: Mikel (6), Cuadrado (6), Remy (6).
Man of the match: Carles Gil