The former England skipper went into the game needing one more goal to become the first man to score 200 times in the Premiership, but he trudged off at the end having had no more than a glimpse of a chance and seen his side's Champions League hopes severely dented.
Saha's 74th-minute equaliser cancelled out Kieron Dyer's 21st-minute strike, but it was scarcely more than the visitors deserved after dominating for long periods.
Indeed, had Shay Given not twice denied former team-mate Saha, the Londoners would have been leaving Tyneside with all three points.
Fittingly, it was England Under-21 midfielder Sean Davis who made the goal on a night when he outshone the more experienced and illustrious men around him in midfield to give Fulham a little more breathing space in their fight for top flight survival.
By contrast, Newcastle's big names drastically under-performed and were booed off the pitch by sections of the home support.
Manager Bobby Robson and his players are confident they can hang on to their advantage to clinch a top-four finish, but while they returned to fourth place with their single point, it is the two which got away which they may come to rue.
There is undoubted talent within the squad, but it was their capacity for self destruction which was more in evidence on a night when the script was well and truly torn up.
Just how United went in 1-0 up at half-time was a mystery Jean Tigana will contemplate for some time after his side out-played their hosts for long periods but - and this is the story of their season to date - could not make the pressure count.
The contribution of Fulham's French connection far out-weighed that of Newcastle's as former Magpie Alain Goma, along with Andy Melville, kept a tight rein on Shearer and Carl Cort at the back, while Steed Malbranque in tandem with
Davis took a firm hold in midfield to give Saha and Steve Marlet a chance to show what they can do.
Unfortunately for Tigana, their repertoire at the moment does not include clinical finishing, and that, combined with more solid goalkeeping by Given, was largely to blame for the deficit.
United's Gallic duo Laurent Robert and Sylvain Distin, who replaced Nikos Dabizas in central defence as Robbie Elliott was recalled at left-back, were less than effective to give the Londoners genuine hope of success.
Fulham full-backs Steve Finnan and Rufus Brevett were allowed to join the attack virtually unopposed, and that left Newcastle stretched too often for comfort.
Given had already had to head away a Davis long ball from Marlet when Malbranque wriggled away from Aaron Hughes and squared for the same man to force a fine tackle from Gary Speed.
But the home side went in front with 21 minutes gone when Robert instinctively headed Shearer's lay off through to Dyer who, with the help of a kindly ricochet and a touch off Edwin van der Sar's legs, put United in front.
But Given snatched the ball off Saha's toe four minutes later as the Magpies defence creaked alarmingly and then got away with a hesitation after Marlet ran on to Brevett's ball over the top.
Marlet directed a close-range shot straight into the keeper's arms after Malbranque again played him in 10 minutes before the break, and it was a relieved Robson who welcomed his players into the dressing room for a much-needed pep talk.
But the pattern of the first half was very much replicated after the restart, as Davis in particular took the game by the scruff of the neck with the United midfield struggling to get to grips with him.
Saha went close on 54 minutes when he left Andy O'Brien for dead and drove into the box only to be denied once again by Given.
Cort had earlier sent a header over form a Nolberto Solano corner and Robert saw a long-range effort deflected wide by Melville with van der Sar stranded, but it was Fulham who continued to dominate as Newcastle laboured.
And they got their reward 14 minutes from time when Robbie Elliott only half-cleared a Malbranque corner and Saha turned Davis' blistering volley past Given.
Jermaine Jenas, a 68th-minute replacement for Cort, shot tamely at van der Sar after being played in on the edge of the box by Dyer 10 minutes from time as United belatedly rallied, but it was the visitors who finished the stronger and with a justifiable claim for disappointment at the draw.