However, beleaguered Queens Park Rangers edged closer to relegation with a lacklustre 3-0 home loss to Liverpool, leaving the last-place club eight points adrift of safety heading into 2013.
Chelsea fell behind to Steven Pienaar's strike after just 63 seconds at Goodison Park but hit back through goals either side of the halftime by Lampard, who is free to talk to other clubs from Tuesday with his contract up in the summer.
A fourth straight win kept third-place Chelsea four points behind Manchester City, and 11 off Manchester United, with a game in hand on both rivals going into the new year.
Rafa Benitez is slowly putting his stamp on the European champions five weeks after joining the club as interim manager but his next task may be to persuade his bosses to hand the 34-year-old Lampard, who has been at Chelsea since 2001, a new deal.
"I just hope for me personally (to) play in a winning team," said Lampard, who has scored in each of his last three starts. "I know there's a lot of speculation and talk . but for me the enjoyable bit is the 90 minutes."
Luis Suarez scored twice in the opening 16 minutes to take his league tally to 13 — one behind top scorer Robin van Persie of Man United — and Daniel Agger added the other for mid-table Liverpool, with all three goals coming in a one-sided first half.
Liverpool manager Brendan Rodgers wasn't at Loftus Road — he was sent home from London hours before kickoff because of illness — but he would have enjoyed watching from afar as Suarez and his teammates ran amok.
"We played probably our best football of the season in the first half," Liverpool captain Steven Gerrard said. "Luis Suarez has been brilliant ... he's a magician."
Liverpool climbed a position to ninth and is five points off fifth-place Arsenal.
Chelsea stayed in the title hunt by ending Everton's nine-month unbeaten run at home, but the visitors will come away from Goodison Park knowing they were fortunate to survive an onslaught by David Moyes' side.
Nikica Jelavic twice struck the goal frame, as did fellow striker Victor Anichebe, as Everton passed up a chance to move ahead of its opponent.
"We've run the European champions really close but we didn't quite have enough in the end," Moyes said. "We played well enough to get a second goal but were unfortunate, having shots back off the woodwork. I thought we were a bit unlucky."
It was left to Lampard to rescue Chelsea, demonstrating the priceless knack of finding time and space in the area that has made him one of the most prolific midfielder in Premier League history.
The England midfielder headed in a cross from Ramires in the 42nd and then was on the spot to scoop home from close range after Everton goalkeeper Tim Howard saved from Juan Mata.
"We have to keep believing this season — there is a long way to go," Lampard said. "We can only win our games, then rely on other things."Suggest a correction