At the other end of the table, Bolton Wanderers crushed Stoke City 5-0 and Wolverhampton Wanderers beat Wigan Athletic 3-1 to inflict the visitors' eight defeat in a row.
Goals from Gareth Bale, Aaron Lennon and Jermain Defoe gave Tottenham their seventh win in eight league matches to move them alongside Chelsea on 22 points, although Spurs have a game in hand on all the teams in the top four.
Tottenham were 2-0 ahead at the break but manager Harry Redknapp, recovering at home after heart surgery, would have suffered as his team hung on grimly after Younes Kaboul's 57th-minute own goal started a Fulham siege.
Tottenham goalkeeper Brad Friedel made several reaction saves, Luka Modric cleared one shot off the line and Fulham had a strong penalty shout turned down after a frantic goalmouth scramble before Defoe scored on the break in stoppage-time.
"He [Friedel] was probably the best player on the pitch," said Fulham manager Martin Jol, who was sacked by Tottenham in 2007 despite consecutive fifth-place finishes and who was warmly applauded by the visiting fans.
"We had 26 or 30 attempts on goal after half-time and yet we just couldn't sneak one in," Jol told Sky Sports. "We deserved at least a point, for sure. At least a point."
Second-half goals by David Edwards and Stephen Ward sealed victory for Wolves after Wigan had equalised just before halftime through Ben Watson.
FORM SLUMP
Wolves, who began the season well before a slump in form which resulted in no league wins since August, had taken the lead through former Tottenham player Jamie O'Hara.
The home side moved up to 13th in the table with 11 points. Wigan are bottom with five points and Bolton failed to move out of the bottom three despite thrashing Stoke.
Chris Eagles and Ivan Klasnic scored twice each to earn Bolton their first home league points of the season and avenge their 5-0 loss to Stoke in this year's FA Cup semi-finals.
Tottenham seemed to be heading for a comfortable victory at Craven Cottage despite never finding their rhythm.
They took the lead when Kyle Walker's low cross reached Bale beyond the far post and the Welsh winger's powerful shot was deflected in by Chris Baird.
Bale then combined well with Lennon on the stroke of half-time, sending the England winger on a surging run before he turned inside Baird and drilled a shot past Mark Schwarzer and into the net.
The second half was almost unbroken Fulham domination and it was no surprise when they reduced the arrears, although Kaboul was unlucky when he unwittingly beat Friedel after Ledley King's clearing header struck him from close range.
Fulham camped in Tottenham's half for the rest of the game and Clint Dempsey came close to equalising when he rounded Friedel but his shot was deflected wide by King.
The 40-year-old Friedel made a series of excellent saves, one in particular from Dempsey from close range which sparked an in
