Leicester moved back above Manchester City as Liverpool's closest challengers after a night dominated by penalty controversy at the King Power.
Jamie Vardy was booked late in the first half when he appeared to have been tripped inside the area.
However, the Foxes were awarded a far softer spot-kick after the break when Jonny Evans went down clutching his face inside the area.
On both occasions a VAR review backed referee Craig Pawson's initial call and Vardy scored for the seventh straight game to open the scoring from the spot.
James Maddison then sealed the points deep into stoppage time to move to within five points of Liverpool at the top of the table.
Chelsea badly missed the presence of Tammy Abraham due to a hip injury in Saturday's shock 1-0 home defeat to West Ham and the return of their top scorer proved the difference against Villa.
Abraham's 26 goals on loan helped Villa get promoted last season and he did not celebrate when heading in Reece James's cross to open the scoring.
Trezeguet bundled home to bring the visitors level before the break, but Abraham then turned provider by chesting down for Mason Mount to brilliant volley high past Tom Heaton.
Wolves remain unbeaten in the league since September and goals from Leander Dendoncker and Patrick Cutrone either side of half-time saw off a disappointing West Ham at Molineux.
Southampton moved out of the bottom three with a second straight win as Danny Ings and Ryan Bertrand won the battle of the bottom two at the beginning of the evening against Norwich 2-1.