Lampard was in the right place at the right time for the ball to bounce off him into the net after Fernando Torres' superb scissors kick careered off the crossbar.
It was the midfielder's 12th goal of the season, his third in as many games since his latest recall to the side and the 181st since he joined Chelsea 10 and a half years ago.
He is now just 12 and 21 goals, respectively, shy of fellow Blues legends Kerry Dixon and Bobby Tambling in the all-time list.
Manager Villas-Boas, who this week insisted he enjoyed a "fantastic" relationship with Lampard amid reports to the contrary, said: "He will continue to threaten all remaining Chelsea records.
"He is almost within a 10-goal distance now from another Chelsea legend and it's good for him."
Suggesting Lampard's goal owed more to instinct than luck, he added: "Frank is always a player who has this amazing timing of arrival in the box.
"It's not coincidence that he's one of the best goalscoring midfielders in the world and his timing is magnificent."
The same cannot be said about team-mate Torres for most of the striker's Chelsea career, but he produced one of the best performances since last year's £50million move from Liverpool.
The Stamford Bridge crowd responded with arguably their biggest show of support yet for a player who is in the midst of another goal drought.
Villas-Boas, who is playing Torres during Didier Drogba's absence at the African Nations Cup, said: "He's getting his good run now of games, finding inspiration, finding motivation, finding form, has all the team behind him and has the fans behind him as you saw today.
"It's good to see that the player is picking up confidence, assisting people. He hasn't been scoring but is getting nearer every time.
"As long as he helps the team to win games, I think we are happy with what he's doing."
Torres had two penalty appeals turned down and was harshly booked for the second of them, but Sunderland also had a decent shout of their own.
Villas-Boas had yet to see replays of any of them but accepted the visitors created plenty of other chances.
"For us to put an end to Sunderland's amazing run of form, it would always take incredible effort from us and it happened," he said, delighted his side had capitalised on draws for Tottenham and Liverpool at the same time as closing the gap to leaders Manchester City to eight points.
"An important weekend for us bearing in mind the weekend's results."
Villas-Boas confirmed Gary Cahill, who attended Saturday's game, was set to complete his move from Bolton on Sunday.
He also hailed the return Michael Essien, who came off the bench to make his first appearance of the season following knee surgery.
Villas-Boas said: "To see a player that makes the switch so quick from a reserve-team game to full Premier League intensity in such a short time, it's amazing.
"You have to compliment our medical department. They've reduced for at least a month Michael's return to football.
"It's very, very gratifying for the team to have him back."
Frustrated Sunderland boss Martin O'Neill was adamant his side's penalty claim, for a foul on Nicklas Bendtner, was legitimate.
"I had a quick flash before I came out at ours and ours is obviously a definite penalty," he said.
"I've been told, certainly, that the first one (on Torres) at our end is not a penalty."
O'Neill was even more upset about the opportunities his side squandered, with James McClean missing an open goal and Craig Gardner and Bendtner also snatching at presentable chances.
"We missed at least five really good opportunities and I think that's too many," he said.
"I know scoring a goal is pretty difficult but it's not that difficult.
"A blundering full-back could've stuck a couple of those in - from about four leagues below."
Insisting he would not panic buy in the January transfer window as a result, he added: "I don't think your immediate reaction would be to race out to get somebody who could score 20 goals. He'd only cost about £35million anyway."
Sunderland lost defender Matthew Kilgallon to an ankle injury at half-time after he landed awkwardly making an aerial challenge.
"He went over on his ankle and I think somebody also landed on top of him," O'Neill said.
"It's really unfortunate for the lad."
O'Neill refused to be too downcast about what was a rare setback since his arrival at Sunderland transformed their season.
He said: "When you consider that Chelsea were overwhelmed at the final whistle, I suppose we take some sort of consolation."
