A crowd of 44,686 thought the 21-year-old had opened the scoring with a stinging 52nd-minute volley, only for the Australian goalkeeper to claw it out of the bottom corner.
Schwarzer also made two good saves from Peter Lovenkrands to preserve his clean sheet on another frustrating afternoon for Chris Hughton's men on their own park.
It could have been worse for the Magpies, who saw Moussa Dembele's 70th-minute volley come back off the crossbar after Tim Krul had kept out three efforts from Clint Dempsey and another from Zoltan Gera.
But they at least claimed another point to add to their survival fund with the total now standing at 18.
St James' Park was something of a fortress for the Magpies last season when they went through the entire campaign without a single defeat on home turf.
This time around, however, their fortunes have been mixed to say the least with thumping victories over Aston Villa and Sunderland having gone hand in hand with depressing defeats at the hands of Blackpool, Stoke and Blackburn.
What the home fans were hoping for was the kind of rousing start their side got off to against Villa and the Black Cats; what they got instead was a nervy opening 45 minutes during which they saw plenty of effort but too little craft.
Man of the moment Carroll was handled well by Brede Hangeland, while the Fulham defence as a unit proved equally resilient.
After a slow start the visitors worked their way into the game as their passing and movement stretched their hosts and it was they who mustered the first serious attempts on goal in a flurry of activity.
First Krul had to come from his line to block Dempsey's close-range effort after Hangeland had flicked on a 28th-minute Simon Davies corner, and he then had to dive full length to turn away Gera's left-foot drive from 20 yards.
He was at full stretch once again on the half-hour to turn away Dempsey's curling shot with Fulham starting to dominate.
However, Newcastle finished the half strongly and might have taken the lead themselves eight minutes before the break.
Danny Guthrie, deputising for the suspended Joey Barton, delivered a corner perfectly into Carroll's run and the striker's volley was unwittingly blocked by team-mate Kevin Nolan on the line.
The rebound dropped to Lovenkrands and he smashed it towards goal only for Schwarzer to save instinctively.
But as the half-time whistle sounded, the anxiety in the stands had decreased little.
The home side needed only two minutes of the second half to call Schwarzer into action once again when Guthrie slid the ball into Lovenkrands' path and his shot was parried by the Australian with Hangeland clearing the loose ball.
Schwarzer was extended even further five minutes later when Carroll ran on to a clearance 22 yards out and blasted in a stinging volley which was heading into the bottom corner before the goalkeeper got down to turn it away.
But Krul had to match his opposite number's feat four minutes later when Dempsey ran on to Dembele's lay-off and fired firmly towards the bottom corner.
However, Newcastle went close once again with 66 minutes gone when Jonas Gutierrez and Guthrie broke at pace for the latter to cross for Lovenkrands, whose firm header was saved by Schwarzer.
Mike Williamson had to make a timely intervention to deny Cottagers striker Andrew Johnson, making his first league start since January, with 69 minutes gone, and from the resulting corner substitute Dickson Etuhu's header was blocked and Dembele rattled the crossbar with a volley.
Hughton threw on the youthful legs of Nile Ranger and Wayne Routledge with time fast running out, but it was Carroll who went closest as time ran down with Hangeland making a priceless block to keep out his 85th-minute strike.
Newcastle Krul, Simpson, Williamson, Coloccini, Jose Enrique,Guthrie (Routledge 76), Tiote, Nolan, Gutierrez, Carroll,Lovenkrands (Ranger 76).
Subs Not Used: Soderberg, Campbell, Smith, Xisco, Steven Taylor.
Booked: Williamson, Tiote.
Fulham Schwarzer, Kelly, Hughes, Hangeland, Duff, Dempsey,Murphy, Davies, Gera (Etuhu 69),Andrew Johnson (Eddie Johnson 89), Dembele.
Subs Not Used: Stockdale, Pantsil, Kamara, Greening, Briggs.
Booked: Hangeland, Murphy.
Ref: Lee Probert (Wiltshire).