Redknapp was missing as he recovered at home after undergoing heart surgery.
Gareth Bale was credited with the first goal after his powerful shot deflected off Chris Baird before Aaron Lennon's clinical finish doubled the advantage.
An own goal by Younes Kaboul, after Ledley King headed against his back, set up a grandstand finish but Jermain Defoe secured victory in stoppage time.
Redknapp's health will not exactly have been helped by a number of goalmouth scrambles in front of Brad Friedel's goal in the closing stages, but Defoe's clinical finish with virtually the last kick of the game made it a good day for the north London outfit, who moved level on points with Chelsea in the Premier League table.Spurs were lucky admits Jordan
Having scored 17 times in their previous seven league games, Tottenham have found goals easy to come by this season and they took the lead with their first noteworthy attack in the 10th minute.
Kyle Walker's burst down the right ended with a lay-off to Lennon, and his cross was pushed by Mark Schwarzer into the path of Bale.
The Wales international's powerful effort from an angle struck Baird, who could do little about stopping the ball cannoning off him into the net.
Fulham are now just one point above the relegation zone but it was a cruel scoreline for Jol's team.
At the other end Friedel had to be at his best to keep out efforts from John Arne Riise and Clint Dempsey.
Tottenham's hard-earned win was summed up by Scott Parker, who battled on after being caught by what appeared to be an accidental Steve Sidwell elbow in the 20th minute.
England boss Fabio Capello looked on concerned as England international Parker received lengthy treatment for a nose wound, but he was able to carry on.
Capello, however, will have been impressed with Lennon's finish on the stroke of half-time which put Spurs in command.
The winger, who has not played for England since the 2010 World Cup, exchanged passes with Bale and burst down the left before cutting inside the area, wrong footing Baird and firing across Schwarzer.
Fulham were not helped by the loss of Zdenik Grygera, who was given oxygen as he left the pitch on a stretcher with what appeared to be a serious knee injury.
But Jol's side showed spirit in the second half wtih Friedel producing a one-handed stop to keep out Brede Hangeland's 52nd-minute header before Kaboul's own goal gave the home side hope.
Kaboul was helpless as King's headed clearance from a corner cannoned off his team-mate and over the line in the 57th minute.Fulham deserved a point - Jol
Fulham piled on the pressure in the closing stages.
In a chaotic goalmouth scramble, Kyle Walker appeared to handle the ball inside his own area while man-of-the-match Friedel again produced an excellent one-handed stop to deny Moussa Dembele.
In addition, Luka Modric making a clearance off the line to deny Dempsey.
Tottenham scored their third deep into stoppage time as substitute Defoe fired home low via a slight deflection from Emmanuel Adebayor's cut-back to wrap up the points.
Fulham's former Tottenham manager Martin Jol:
"I thought we deserved at least a point. Tottenham had three attempts on goal in the first half and scored two goals.
"We must have had 26 or 30 attempts after half-time. He (Friedel) was probably the best player on the pitch, but if you don't score then you have a problem.
"Of course I heard the applause from the Tottenham fans. But I don't want to make a meal of it. I'm happy here."
Tottenham winger Gareth Bale:
"It's always nice to score and keep the run going. I am claiming the goal. I've seen it a few times and it's definitely my goal.
"We knew how hard it was going to be. Fulham played very well and put us under the cosh, but we showed our character.
"In recent years we would have conceded more in the second half, but we have belief in ourselves."