The 5-1 defeat means Fulham have now gone 15 months, three managers and 26 away games since a victory on the road.
Keane fired Spurs ahead midway through the first half and Huddlestone got his first, two days before his 21st birthday on the stroke of half-time.
Clint Dempsey gave Fulham a chance with his goal but Keane, Huddlestone and Jermain Defoe made sure of the thrashing in the final 20 minutes.
Tottenham were boosted by the return to form of skipper Ledley King who was making his first start in a Spurs shirt since May.
Three former Spurs players lined up for Fulham - Simon Davies, Paul Konchesky and Danny Murphy - while Steed Malbranque used to ply his trade at Craven Cottage.
There was a flat start to the game with both sides struggling to create any real chances in front of goal.
Fulham looked nervous as they went in search of their first win on the road in 2007, but created the first chance on goal on six minutes.
Alexei Smertin and Konchesky linked well and played the ball to American Dempsey who shot from 25 yards over the bar of Paul Robinson's goal.
For all of Spurs' pressure they failed to create any clear-cut chances until the 24th minute when Malbranque crossed for Dimitar Berbatov whose header had Fulham keeper Antti Niemi at full stretch to keep it out.
But two minutes later the hosts eventually took the lead. Huddlestone crossed for Pascal Chimbonda who headed the ball into the path of Malbranque. His shot cannoned off the post and into the path of Keane who tapped the ball into an empty net.
The goal was no more than Spurs deserved and they continued to pile on the pressure. Malbranque went close when he headed a Keane cross but it was well-saved by Niemi.
They doubled their lead on the stroke of half-time when Malbranque crossed for Berbatov who laid the ball back to Huddlestone who shot from 30 yards through a host of Fulham bodies and past a motionless Niemi.
Fulham were handed a lifeline when Dempsey bundled the ball home from six yards past Robinson on the hour mark, but a minute later Keane went to the other end to tap-in a Berbatov header from Jamie O'Hara's corner.
The result was wrapped up in the 70th minute when Huddlestone grabbed his second in spectacular fashion. Aaron Lennon played in the England Under-21 international and he volleyed from the edge of the box into the far corner of the net.
Defoe came off the bench to get the fifth goal in the 90th minute to compound Fulham's misery.
To make things even worse for Fulham they had Moritz Volz sent off at the death for his second bookable offence.
The result continues Spurs' revival under Juande Ramos and was the perfect reply to their derby day defeat to Arsenal.
Fulham are a club in freefall though, no manager, no win since the beginning of November and on this performance no chance of being a Premier League club next season.