Bobby Zamora marked his Fulham debut with a stunning strike as Celtic's pre-season preparations suffered a setback at Craven Cottage.
Zamora completed his move from West Ham on Tuesday and wasted no time opening his account when he unleashed an unstoppable drive from the edge of the area.
A moment of brilliance from strike partner Erik Nevland set up the chance and the Norwegian also got on the scoresheet with a well-taken opener.
Celtic dominated between the first-half goals and deserved their 42nd-minute response from Barry Robson, who curled home a slick free-kick.
But the outcome was put beyond doubt when Denmark defender Leon Andreasen powered home with five minutes to go.
It was a surprisingly competitive match that the Scottish champions, fielding a strong team, controlled for lengthy spells.
But in contrast to Fulham's clinical touch, they missed a string of chances in the first half and struggled to re-establish themselves in attack after the interval.
Celtic boss Gordon Strachan included 10 of the starting line-up which dispatched Southampton 2-0 last night, with Massimo Donati replacing Paul Hartley in midfield.
Most of team was substituted at half-time at St Mary's but their exertions may have explained the early defensive lapse that allowed Fulham to take an early lead.
Just one minute and 47 seconds were on the clock when Nevland escaped unnoticed into the box.
New signing Zoltan Gera picked out Nevland with a floating cross from the right and the little Norwegian striker buried the chance from close range.
Scott McDonald had a chance to equalise shortly after but blazed over the bar as he raced in at the right post.
Sharp reflexes from David Stockdale, a recent capture from Darlington, denied Robson from the edge of the area as Celtic took control of the game.
McDonald glanced a header wide and then Chris Killen directed a fine chance straight into the arms of a grateful Stockdale.
Just as it seemed Fulham's early exuberance had been tamed by Celtic, they conjured a stunning goal initiated by Paul Konchesky's long pass to Nevland.
Nevland, stationed near the byline, whipped the ball over his head to the edge of the area where the onrushing Zamora drove home a magnificent strike.
Zamora was growing in confidence and his delicate flick to Andranik Teymourian should have been buried by the Iranian, but keeper Mark Brown came to the rescue.
Fulham were back on top but then it was Celtic's turn to score against the run of play, Robson converting a free-kick after being felled by Brede Hangeland.
The match bore little resemblance to a pre-season friendly amid a competitive opening to the second half.
Replacements had been kept to a minimum by both managers at half-time but by 66th minute the Cottagers line-up looked markedly different.
Celtic laid siege to the opposition goal for several minutes but could not breach a determined defence.
Instead, they were shown the way it should be done in the 86th minute when a succession of corners eventually saw the ball drop to Andreasen who made no mistake.
Roy Hodgson claimed Bobby Zamora is determined to prove himself after the new Fulham striker fired a stunning goal in today's 3-1 victory over Celtic.
'It was a wonderful goal created by a nice move. It's a good start for Bobby,' he said.
'He had a difficult time last season and needs a new start. He needs to put last season totally behind him.
'We'll work on him becoming the player he was before last season. We're getting a man who is very motivated to show he is a top-class Premier League player.
'He did enough in his first 45 minutes today to suggest we'll get some good use out of him.'
Zamora cost Fulham £6.3million, although the deal also included John Pantsil moving from Upton Park to Craven Cottage.
Andranik Teymourian, Zoltan Gera, David Stockdale and Mark Schwarzer have also joined during the transfer window but Hodgson revealed his summer spending spree is not over yet.
'There won't be many more signings but we haven't ruled out bringing in a couple more in key positions to help us out,' he said.
'We've done quite a few things already and I'm very pleased with what we've done.
'We're looking at another striker and flirting with the idea of a defensive midfield player.
'We may also need some cover at centre-back because we're fairly light in that area. If we resolve those three situations we will have a strong squad.'