The champions stay nine points clear of Manchester United, who crushed West Bromwich Albion 3-0 at home, and 15 in front of Liverpool and Tottenham Hotspur who both notched up 2-0 home victories.
William Gallas and midfielder Frank Lampard put Chelsea ahead but Fulham came back into the game with a strike from Brian McBride before the half hour and a 56th-minute penalty converted by Heidar Helguson.
Chelsea manager Jose Mourinho, referring to his team's reaction to Fulham's fight-back, told reporters, "When you are in a comfortable position and you make mistakes, it is hard to come back but I trust my players' mentality."
Fulham manager Chris Coleman told Sky Sports, "I thought we showed tremendous spirit, and courage, and we got back. Then the game could have gone either way."
Paul Scholes, Rio Ferdinand, who headed his second goal for United, and Ruud van Nistelrooy scored at Old Trafford where manager Alex Ferguson was as impressed by his defense.
"Our defending has been good in the last few games. We've hopefully come out of that bad spell," he told United's official website after a third successive league clean sheet.
"The result in Benfica was a killer for us but we've turned it around for ourselves," he added, referring to United's 2-1 loss in Lisbon earlier this month that put his side out of Europe.
At Anfield, Michael Owen had an unhappy return to his former club with Newcastle United, who went down to two first half goals and had midfielder Lee Bowyer sent off for an ugly tackle on Xabi Alonso.
Steven Gerrard struck after a quarter of an hour and two minutes before the interval Peter Crouch's shot came back off the post but went in after hitting prostrate keeper Shay Given on the back of the head.
"We got off lightly. We were played off the park in the first half and 2-0 certainly didn't flatter them at halftime," Newcastle manager Graeme Souness was quoted as saying on club's official website.
"They peppered our goal and we've got to learn from that."
Arsenal ended a run of three league defeats in which they had not scored by winning 1-0 at Charlton Athletic to climb to seventh, 20 points adrift of Chelsea and two behind Bolton Wanderers, held 0-0 by bottom team Sunderland, and Wigan Athletic, who edged a thriller with Manchester City 4-3.
Jose Antonio Reyes scored just before the hour to end the drought with his second league goal of the season, a shot inside the near post after goalkeeper Thomas Myhre had parried Thierry Henry's effort from the right.
"The team was a bit nervy because we have lost a few games recently... When we scored it was a relief and we are not used to this but this victory can give us a new start," manager Arsene Wenger told the Arsenal website.
Charlton were down to 10 men for the last 18 minutes after midfielder Danny Murphy was sent off for dissent.
Spurs beat 10-man Birmingham City with a Robbie Keane penalty and Jermain Defoe's injury-time strike. City's Muzzy Izzet was sent off just past the hour for a second bookable offence.
Aston Villa beat Everton 4-0 at home with two strikes from Czech Milan Baros, who admitted to handball in the build-up to the opening goal of the match.
Striker Shefki Kuqi scored both for Blackburn Rovers in their 2-0 win at Middlesbrough and Jason Roberts also hit two in the thriller at Wigan Athletic which the home side edged 4-3 against Manchester City after leading 4-1.
Portsmouth manager Harry Redknapp remained unbeaten in two home matches since his return to the club after a 1-1 draw with West Ham United, while Sunderland picked up only their sixth point in 18 matches and first in 10 against fifth-placed Bolton.