Christian Benteke put Villa ahead in the 14th minute, but Lampard beat American goalkeeper Brad Guzan with a curling shot in the 61st minute and scored from close range in the 88th.
A 34-year-old midfielder, Lampard has 203 goals since joining Chelsea in 2001, one more than Bobby Tambling scored from 1958-70.
Chelsea (21-7-9) is third with 72 points with one league game left, five points ahead of Arsenal (19-7-10) and six in front of Tottenham (19-8-9).
American defender Eric Lichaj made his first start for Villa since an FA Cup match against Millwall on Jan. 25 and his first Premier League start since Dec. 29 versus Wigan.
Chelsea’s Ramires was ejected in the 45th and Benteke in the 58th, both for their second yellow cards.
The Associated Press