The leaders swept the injury-plagued Black Cats aside, racing into a 4-0 lead inside 34 minutes despite the absence of African Nations Cup quartet Didier Drogba, Michael Essien, John Obi Mikel and Salomon Kalou.
Anelka set the ball rolling with just eight minutes gone, rounding keeper Marton Fulop to make it 1-0, and Florent Malouda doubled his side's advantage with a superb solo effort nine minutes later.
Full-back Ashley Cole had the Stamford Bridge crowd on their feet once again with 22 minutes gone when he controlled John Terry's pass and dummied the covering Daryl Murphy before beating Fulop. That was the Premier League's 18,000th goal.
Cole then set up Lampard to volley home a fourth 11 minutes before the break.
Michael Ballack added a fifth seven minutes after the restart, and although substitute Bolo Zenden pulled one back against his former club four minutes later, Anelka helped himself to his second when he made the most of Fulop's misdirected 65th-minute punch.
Lampard wrapped up the rout at the death and Darren Bent's injury-time strike proved scant consolation.
Under-pressure Liverpool boss Rafael Benitez was left to reflect upon what might have been as his side threw away a precious victory at Stoke.
The Reds were leading 1-0 with just seconds of normal time remaining when Germany international Robert Huth stabbed home an equaliser amid a late assault.
Benitez saw defender Sotirios Kyrgiakos fire the visitors in front with his first goal for the club with 57 minutes gone.
But after Huth struck, he could only look on helplessly as Dirk Kuyt headed against a post when he really should have scored in the sixth minute of stoppage time at the end of the game.
New Burnley boss Brian Laws saw his side hold Manchester United at Old Trafford for 64 minutes before they finally succumbed to Dimitar Berbatov.
The Bulgaria international linked with Wayne Rooney before his shot was deflected past keeper Brian Jensen by defender Michael Duff, and further goals from Rooney and substitute Mame Biram Diouf - his first for the club - made sure of the points.
Wolves were forced to play the entire second half with 10 men after having Richard Stearman sent off for a second bookable offence in injury-time at the end of the first when he pulled back Wigan's James McCarthy.
Keeper Marcus Hahnemann saved Hugo Rodallega's resulting penalty and Paul Scharner blasted the rebound wide, but McCarthy finally beat the American on the hour, pouncing on Rodallega's parried shot.
Wigan midfielder Hendry Thomas was later sent off for a second yellow card offence after a foul on Steven Ward, but his side doubled their lead through Charles N'Zogbia with 17 minutes remaining.
Fifth-placed Tottenham could not find a way past lowly Hull as Harry Redknapp's 500th Premier League game ended in stalemate with Tigers keeper Boaz Myhill turning in a fine individual display.
Meanwhile, bottom of the table Portsmouth's home clash with Birmingham was called off this morning because of a waterlogged pitch at Fratton Park.