The 34-year-old held off the attentions of Nathan Baker and Ashley Westwood to equalize against the relegation-threatened side and pull level with the 43-year-old record, before completing the comeback with a neat finish from Eden Hazard's cutback as the game entered stoppage time.
The 61st-minute goal was Lampard's 10th in the Premier League this season, and his 17th in all competitions, as he marked reaching double figures in the league for the 10th successive season.
Tambling, now 71 years old, was presented to the Stamford Bridge crowd at Chelsea's home game against Swansea on April 28, which saw Lampard score his 201st goal from the penalty spot.
The former striker notched the total in 370 games over a 12-year stay at Chelsea, while Lampard broke the record on his 606th appearance for the club.
Lampard has been afforded a reduced role this term under interim manager Rafael Benitez, making just 20 starts, but his double against Villa all but confirms Chelsea's place in the Champions League next term due to its superior goal difference over fifth-placed Tottenham.