The Australia international kept out Darren Bent's first-half free-kick and then blocked Alan Hutton's left-foot effort after the break to ensure the game ended goalless.
Substitute Bolo Zenden and Hutton both fired into the side-netting as the home side make a late push, but the first of four successive home games which boss Steve Bruce believes will define the club's season ended in stalemate in front of a frustrated crowd of 40,192.
The point lifted the Wearsiders three clear of the drop zone, but there is little doubt that Roy Hodgson will have been the happier manager as his team extended their unbeaten run in all competitions to eight games three days after they secured their passage to the last 16 in the Europa League.
The game had been billed in certain quarters as a showdown between England hopefuls Bent and Bobby Zamora as they attempt to force their way into Fabio Capello's World Cup plans.
In the event, both men were largely anonymous in a first half which was notable only for a woeful lack of quality.
Bent and strike-partner Kenwyne Jones got little change out of Brede Hangeland and Aaron Hughes, while at the other end, Zamora - playing ahead of Zoltan Gera - was equally unable to extend Michael Turner and John Mensah.
Chances were few and far between with Gera curling a seventh-minute effort just wide and Zamora looping a header harmlessly off target for the visitors with 26 minutes gone.
Schwarzer did have a save to make, but that did not come until the 40th-minute.
Having seen Jones blast high over from 20 yards two minutes earlier, the Australian found himself in the firing line when Hangeland was penalised for a challenge on Jones just outside the box.
Bent curled a well-struck free-kick around the defensive wall, but the keeper was well positioned and although he could not hold the ball, his defenders mopped up before any damage was done.
But meaningful action inside either penalty area was a rarity as the game was fought out largely in the middle third, where Fulham skipper Danny Murphy was the most influential figure.
Even he, however, could not find the killer pass to open up the home defence as an attritional battle unfolded with Hutton, Kieran Richardson and Chris Baird all booked for fouls before the break.
The pattern of the first half was repeated during the early stages of the second with neither side able to put together a sustained period of pressure.
Returning midfielder Lee Cattermole played his side into trouble went he lost out to Simon Davies on halfway with six minutes of the half gone.
Davies played Zamora into space down the right and then got into position to receive the ball back, although his shot was blocked at source.
Bruce replaced Cattermole with Zenden as he looked to inject some urgency, with the newcomer lining up on the left as Richardson moved inside.
The Dutchman also had an instant impact, combining with Jones to set up full-back Hutton, who stepped inside before forcing Schwarzer into a save with a low left-foot drive.
Murphy limped off to be replaced by Jonathan Greening three minutes later, and Jones went close with an 18-yard snapshot within seconds.
But as time ran down, it was Fulham who had the greater craft and composure with the home fans growing increasingly restless.
Newcastle old boy Damien Duff saw a 69th-minute effort deflected just wide, but Bent only just failed to get on the end of Turner's ball over the top three minutes later.
Zenden got a shot in after Hughes could only help on keeper Craig Gordon's 74th-minute clearance, but his effort from a tight angle ended up in the side-netting.
Hutton did the same from the other flank as he met Zenden's driven cross at full-stretch seven minutes later with the Black Cats belatedly establishing a momentum.
Fraizer Campbell might have snatched a precious victory with three minutes remaining, but he skied his shot high over as another two points slipped away.