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 1959-70.
"It means everything. It's amazing," said Lampard, whose contract expires at the end of the season. "The support I've had from teammates, you saw that at the end, and I'm thankful to every one of them because they're the ones that put it on a plate for me sometimes. And the fans, they've been with me for a long time and were probably frustrated alongside me not getting there so I'm just delighted."
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 by referee Lee Mason, both for their second yellow cards.
Chelsea defender John Terry left on a stretcher after an injury that could jeopardize his hopes of playing in the Europa League final Wednesday against Benfica. That will be the 68th game of the season for Chelsea.
Also, West Ham manager Sam Allardyce ended uncertainty about his future by signing a new two-year contract with the Premier League club.
BERLIN (AP) American defender Steve Cherundolo has set a Hannover record for Bundesliga appearances.
The 34-year-old from San Diego, a member of the last three U.S. World Cup teams, appeared in his 299th Bundesliga game in a 3-1 loss at Bayer Leverkusen, one more than the mark Juergen Bandura set from 1964-74.
Cherundolo joined Hannover in 1999, when it was in the second division, and helped it earn promotion to the Bundesliga for the 2002-03 season.
Hoffenheim lost 4-1 at home to Hamburg and remains in the relegation zone with one game left, two points behind Augsburg and Fortuna Duesseldorf.
Werder Bremen clinched Bundesliga status for next season with a 1-1 tie against Eintracht Frankfurt.
Already relegated Greuther Fuerth wasted an early lead and lost 2-1 to visiting Freiburg and became the first club in the Bundesliga's 50-year history to go winless at home (0-13-4).
PARIS (AP) Marseille defeated Toulouse 2-1 on goals by Andre Ayew in the 45th and 62nd minutes, preventing Paris Saint-Germain from clinching the league title until at least Sunday.
PSG (22-5-8) has a four-point lead over Marseille (21-8-7), which has two games left. PSG is at third-place Lyon (18-8-9) on Sunday and can ensure its first league title since 1994.
Marseille is assured of no worse than third place and a berth in the qualifying round of next season's Champions League.
Eden Ben Basat scored in the 82nd minute for Toulouse.
Monaco clinched promotion to the top division with a 1-0 win over Nimes.
MILAN (AP) On the day it was presented with the trophy for its record 29th Serie A title, Juventus was held to a 1-1 tie by Cagliari.
There was a party atmosphere at Juventus Stadium, with Juve players walking out of the tunnel holding their children.
Victor Ibarbo put the visitors ahead in the 12th minute, but Mirko Vucinic tied the score in the 61st.