The England midfielder, restored to the starting XI ahead of Wednesday's Europa League final, cancelled out Christian Benteke's opener with a sweet left-footed effort just after the hour mark before sealing the points - and the record - with close-range effort three minutes from time.
That left him with 203 career goals for the Blues, a fitting landmark forged over 12 years at Stamford Bridge.
Victory in a dramatic match that saw both Ramires and Benteke sent off for two yellow cards effectively assures Chelsea's Champions League status next season, while leaving Villa still in the relegation equation.
The first half had been such a different story, Villa ending it 1-0 up and with a man advantage. Benteke was proving his usual handful in attack too, winning nearly everything in the air, and it was no surprise to see him on the scoresheet in the 15th minute.
He beat Gary Cahill to a Brad Guzan clearance and then peeled off at speed to take Yacouba Sylla's return pass. The Belgian then glided past Cahill with ball at feet and slipped his shot past Petr Cech at the near post.
On the half-hour Lampard came desperately close to his landmark goal, seeing a low free-kick squirm out of Guzan's hands and roll gently against a post. Chelsea were starting to find their feet in the game when a series of refereeing decisions took centre stage.
The first saw Benteke booked rather than sent off for an elbow on Cesar Azpilicueta, before Terry also shown yellow despite seeming to be the last man when he felled Sylla. Lee Mason did flourish red just before the interval though, with the struggling Ramires earning a second booking for high feet on Gabriel Agbonlahor.
Villa's extra man lasted only until the 58th minute, Benteke the man to go this time, again for a second yellow and again for high feet. Within two minutes the scores were level and Lampard was celebrating his long-awaited record-equalling goal. Eden Hazard rolled him the ball from the right flank, he shepherded it into a more central position and then fired home a curling left-footed effort. He was duly mobbed by team-mates as he ran to the away support to take in the moment.
Terry departed on a stretcher after suffering an injury which will place his own Europa League final hopes in severe doubt, but Lampard was yet to have his final say on proceedings. The winner came from a fine Chelsea move, Hazard taking in a one-two in left channel before cutting the ball across goal for Lampard. As so often in his Chelsea career, he was in the right place at the right time and he tapped home with ease.
Source: PA
Source: PA