Newcastle had to come from behind after a Brian McBride goal threatened to ruin Michael Owen's Newcastle debut.
McBride scored from close range after a catalogue of Newcastle errors.
Owen had few chances but his darting run did win the free-kick that led to Newcastle's equaliser, Charles N'Zogbia scoring with a curling shot.
Both sides hit the bar from free-kicks, Stephen Carr for Newcastle and Claus Jensen for Fulham, while Scott Parker was sent off late in the game.
Despite the euphoria that greeted Owen the England striker had an uncomfortable start to his Newcastle career.
Owen barely touched the ball in the opening 15 minutes and when he did finally get hold of the ball he was fouled by Carlos Bocanegra, whose crude lunge earned him a booking.
Owen's frustration increased when Fulham goalkeeper Tony Warner was unable to gather a Newcastle corner, but the ball arrived too quickly for the England striker to control it.
With 12 minutes remaining Owen began to repay some of his £17m transfer fee when his weaving run brought the free-kick from which N'Zogbia equalised.
N'Zogbia, who had come on for the injured Alberto Luque, flighted a curling shot past Warner, the first goal Newcastle have scored in the Premiership since 4 May.
The concluding minutes of the first half saw Newcastle lose both Luque and Taylor through injury.
Luque had been responsible for creating Newcastle's best chance in the opening half when his curling pass freed Alan Shearer, whose low shot was diverted past the post by Warner.
Taylor collided with the post after he cleared a Tomasz Radzinski shot, an effort that would not have counted as the Canadian had been ruled offside.
Taylor managed to play on but he failed to emerge for the second half.
Newcastle had given an indication of their defensive nerves in the opening minutes when Carr needlessly gave away a corner.
But Taylor's mistake proved altogether more costly.
The Newcastle defender's backpass was too short for Given enabling Radzinski to intercept and lay the ball back to Luis Boa Morte.
The Portuguese winger quickly turned the ball back into the box and Titus Bramble and Jean-Alain Boumsong, who slipped, allowed McBride to sidefoot into the net.
As Newcastle laboured Fulham continued to create the more dangerous chances and Papa Bouba Diop's long-distance shot almost surprised Given, who made an unconventional save with his knees.
Early in the second half Fulham contrived to create three good chances.
First Radzinski broke clear to be denied by Given, then Diop hit the post with a header, while McBride went close with a header after a Boumsong mistake.
Fulham Substitute Collins John almost scored with his first touch, his shot going narrowly wide of the post.
Both sides had chances in the closing stages, notably Fulham through Jensen's delicately flighted free-kick which rebounded off the bar.
The game had a bitter ending for Newcastle when Parker was red-carded for a second bookable offence.
Newcastle manager Graeme Souness: "We spoke what it would be like with Michael making his debut.
"Some of us got a bit caught up in the media hype and we didn't start right and gifted them an early goal.
"Ideally I would have preferred Michael's debut to have been away from home, so I'm pleased this is out of the way. We can now work on his fitness."
Fulham boss Chris Coleman: "It looked like only one team was going to win until we were caught out by Charles N'Zogbia's wonder strike - we just had no luck.
"We took the game to Newcastle from the start and I thought we were excellent.
"We gained more than a point because this it was a fantastic performance - we looked more dangerous."
Newcastle: Given, Taylor (Bowyer 45), Boumsong, Bramble, Babayaro, Carr, Faye (Clark 72), Parker, Luque (N'Zogbia 35), Shearer, Owen.
Subs Not Used: Elliott, Harper.
Sent Off: Parker (83).
Booked: Parker, Faye, Bowyer, Clark.
Goals: N'Zogbia 78.
Fulham: Warner, Volz, Knight, Bocanegra, Niclas Jensen, Radzinski (John 70), Claus Jensen, Diop, Malbranque, Boa Morte, McBride (Helguson 81).
Subs Not Used: Batista, Elrich, Christanval.
Goals: McBride 13.
Ref: A Wiley (Staffordshire).