Christian Benteke had put Villa ahead early on before Ramires saw red just before the interval for Chelsea.
Then Benteke went from hero to villain as he also picked up a second yellow card and within minutes Lampard had struck to level matters before he claimed his own place in Chelsea history when he tapped home from close-range in the final minute.
Villa's opener came with their first real shot in anger just 15 minutes in, and it was that man Benteke. The Premier League's leading goalscorer in 2013 played a nice one-two with Yacouba Sylla and ran at Chelsea's defence - Gary Cahill offered him the outside, and he took the invitation to go past the England defender before slotting home at Petr Cech's near post.
Chelsea looked for a reaction and Brad Guzan kept his side ahead with a couple of crucial saves.
First Juan Mata's delicious lobbed ball sent Demba Ba clear but the American was off his line quickly to save at the striker's feet almost before he could get his shot away.
Then Guzan was at full stretch to deny Lampard, who hammered a low free-kick which skidded off the wet surface heading for the corner. The Villa man palmed it away and off the post, and was even able to react and save the follow-up.
Referee Lee Mason was then at the centre of the action, as Benteke - who had a storming game - was yellow carded for a clear elbow on Cesar Azpilicueta when he could easily have seen red. But the Villa Park crowd did not have long to wait for somebody to receive their marching orders as Ramires got his second yellow for a high challenge on Gabriel Agbonlahor.
Chelsea brought David Luiz on at the break, but they struggled to get a foot-hold in the game - that was until the hour mark when Villa were reduced to ten men and it was Benteke who saw red for his second booking, and another high challenge - this time on John Terry.
Suddenly the game was turned on its head as within minutes, Chelsea were level and it was Lampard who struck to equal Tambling's club record total of 202. He picked up the ball from Eden Hazard on the edge of the box and moved it onto his left before firing into the top corner.
Chelsea thought they had taken the lead with 15 minutes left, but Sylla and then Ashley Westwood saved on the line from Gary Cahill and Demba Ba with Guzan beaten. Nathan Baker also appeared to handle the ball in the incident - but nothing was given.
Captain Terry, making a rare start, was stretchered off after Baker collided with him, as Chelsea pushed looking for the winner. Lampard headed over from Hazard's cross when he should have hit the target, whilst Mata curled a free-kick just wide, Luiz tested Guzan and Cech saved well from Andreas Weimann as the game looked destined for a draw - until that man stuck again in the final minute of normal time to snatch the win.
Lampard began the move on the edge of the box as he played in Hazard, who played a one-two with Ashley Cole before darting into the box and squaring for the England midfielder to tap home and score his 203rd goal and move ahead of Tambling.
Whilst the loss means Aston Villa remain just five points ahead of the relegation spots, Chelsea are now all but assured of a place in next season's Champions League.