The Black Cats twice came from behind as Wahbi Khazri and Fabio Borini's efforts cancelled out goals from Andre Ayew and James Collins.
A point is unlikely to change what appears to be inevitable relegation despite Hull City and Swansea City losing, David Moyes's men are still nine points from safety with just six games left.
West Ham sit nine points clear of third from bottom Swansea, having failed to beat Sunderland.
From minute one Sunderland showed a greater level urgency and willingness to attack in numbers. Javier Manquillo botched a promising attack from kick off when the make-shift left back took too long cutting back poorly to no one in red and white.
The resulting West Ham break saw captain Lee Cattermole taking one for the team tripping up Ayew on the edge of the area before he could put Carroll through on goal, in the first minute.
Despite their greater intent the Black Cats conceded in the fifth minute. Ayew converted a miss-hit Carroll shot from close range, no Sunderland player was near him.
Khazri's dead ball expertise lifted Sunderland almost instantly, the returning John O'Shea wasted an excellent delivery as he flicked on tamely straight at Darren Randolph.
It took a while for the Wearsiders to re-motivate themselves after falling behind, letting the visitors enjoy a lion's share of possession. Robert Snodgrass ended one of the Hammer's best passing moves, shooting wide trying to outfox Jordan Pickford at his near post from 20 yards.
Thankfully Sunderland improved. Darron Gibson wasted a well executed set play, slipping before hitting high and wide, from a smart Khazri cutback.
It was the largely disregarded Khazri who provided the magic to end Sunderland's miserable goal drought. The Tunisian's wind assisted corner evaded everyone, including goalkeeper Darren Randolph who was pinned onto his line by Victor Anichebe backing in.
A genuine turning point the home side, were the better side until half time. Billy Jones shot harmlessly wide cutting onto his left as Sunderland continued to pile men forward.
They were however fortunate to avoid conceding on the break, when Ayew missed from close range. Slaven Bilic's men pounced on a loose Didier Ndong pass to no one, to get in behind Sunderland. Carroll kept alive Snodgrass's dangerous ball across goal, Ayew's half-volley went narrowly over. The Ghanian couldn't manage a clean connection adjusting to a ball played just behind him.
Cattermole saw a decent penalty claim waved away as he collided with Snodgrass in the area after exchanging passes with Anichebe. Khazri missed a great chance, not getting enough purchase on his attempt to place beyond Randolph, he was through after being teed up by Jermain Defoe.
Once again Sunderland conceded just after half time. Unforgivably switching off allowing James Collins to glance in a Robert Snodgrass corner inside six yards, under no pressure.
The game fell flat after Collins's goal, West Ham once again enjoying plenty of possession without creating any real opportunities. Moyes's men looked short of the quality to pin West Ham back as 20 minutes passed without incident.
When Sunderland did improve with time running out unsurprisingly Khazri was the inspiration. The 26 year old shot over from a long range free kick, marking Sunderland's first effort of the half.
The former Bordeaux man then wriggled past two West Ham players to set up Ndong. Unforgivably Ndong shot well over leaning back as he fired unmarked, wasting a massive chance.
Defoe was unfortunate, his stretching effort from close range was blocked by Jose Fonte, the Portuguese just denying Defoe, who had reacted quickest to a half-cleared Manquillo cross.
After a long delay, following Jones's concerning head injury, Sunderland scored from nowhere. Substitute Borini blasted into an empty net, following Randolph's howler. The Republic of Ireland international could only parry to the Italian at full stretch after initially spilling a long hopeful ball under pressure from Anichebe.
Late into ten minutes added on Khazri wasted his chance to be a hero, from a late free kick. He shot well wide from 30 yards wasting a golden chance to cross into a dangerous area much like he did for his goal.
Anichebe missed wide a minute from time, cutting onto his left foot his shot fizzed just wide ending Sunderland's chances of an unlikely victory.
For all the effort and excitement Sunderland couldn't create that one killer chance in the final five minutes. Drawing a game they needed to win, the home side showed greater positivity but still lacked the quality needed to beat Premier League opposition.