Fernando Torres, David Luiz and Branislav Ivanovic were on target as Chelsea took a commanding half-time lead and Lampard, Ramires (two), Oscar and Eden Hazard added to Villa's woes as the Blues moved up to third.
Lampard's strike took him past Bobby Tambling to become the Blues' all time top scorer in the top division and he was delighted to put his name in the club's history books.
"It means I'm old," Lampard joked of the record. "No, it means a lot. I've been fortunate to play for a great club and the managers had team-mates around me.
"I'm very proud of that goals record, to beat a great man such as Bobby who is an absolute legend and a lovely bloke, it means everything.
"Coming across London is not always easy but they (the fans) have supported me from the first minute. I appreciate it. I try to play well for them."
Reflecting on the ruthless demolition of Villa, Lampard said: "We showed great appetite for the game from the first minute.
"(With) our desire to be quick with the ball, the early goal helped. We are enjoying playing again and we needed that attitude to get us out of the sticky patch we were in."
The 34-year-old midfielder will be out of contract at the end of the current season, but Lampard insists he is not thinking about his long-term future.
"No, I'm not concentrating on that far ahead," he said. "I'm under contract here. I'm going to keep going game by game. I love playing here. I'm pleased to be fit and I will keep trying to enjoy my football.
"I believe I have a lot in me to go.
"I don't want to get too deep. The club's position is their position. I'm here to play football to show people what I can do."