Altidore's dismal goalscoring record now stands at one in 41 appearances for the club after he somehow contrived to fluff an effort from three yards out with the goal at his mercy.
Jordi Gomez put the home side in front with a 22nd-minute penalty but Stewart Downing dragged the Hammers level five minutes later with a deflected effort from the right flank.
Connor Wickham saw an 85th-minute drive tipped over by Hammers keeper Adrian but the best chance of a winner - Altidore apart - fell to former Newcastle star Andy Carroll.
Fresh from his resurgent performances against Swansea last week, Carroll hit a low drive from the edge of the box which passed Costel Pantilimon's left-hand post by inches with 89 minutes on the clock.
The Hammers had travelled north in buoyant mood on the back of three straight wins that had lifted them to the improbable heights of fourth place, and with top scorer Diafra Sakho restored to their starting line-up.
And the visitors quickly took control of the game against a home side struggling for goals and also possibly fatigue after a gruelling trio of fixtures against Chelsea, Manchester City and Liverpool.
Anthony Reveillere's wayward defensive header let in Carl Jenkinson in the sixth minute but the on-loan Arsenal man saw his volley blocked by Pantilimon before Wickham booted clear.
Carroll made his first impact on the game in the 10th minute when he met a left-wing cross by the lively Aaron Cresswell with a header which squirted high and wide of target.
The hosts snatched the lead out of nothing in the 22nd minute when referee Phil Dowd pointed to the spot after James Tomkins was adjudged to have tripped Adam Johnson on the right side of the West Ham boss.
Angry Hammers boss Sam Allardyce had to be calmed by Dowd after Gomez duly put the Black Cats in front with a low spot-kick to keeper Adrian's left.
But seven minutes later the visitors were level when north-east native Downing cut in from an apparently unthreatening position on the right flank and hit a low shot which deflected off Gomez and flashed across Pantilimon into the back of the net.
Sakho shot wide from a tight angle in the 38th minute before Altidore's moment to forget, the big American making a complete mess of a cross from the right by Sebastian Larsson as he stood no more than three yards out from an unguarded net.
A low-key start to the second half saw few clear-cut chances for either side, with a Johnson free-kick punched clear by Adrian then Cresswell pushing a shot under Pantilimon at the other end only for the Sunderland defence to boot clear.
Altidore's afternoon to forget came to an end in the 62nd minute when he was replaced by Steven Fletcher and two minutes later Carroll came close for the Hammers with two quick-fire efforts, the second of which saw a lofted shot beat Pantilimon but land on the roof of the net.
Sunderland had a strong penalty appeal rejected in the 71st minute after Santiago Vergini's high ball into the box appeared to strike Winston Reid on the arm, then came Wickham's rising effort from which the visitors were fortunate to emerge unscathed.
Carroll came so close to being the hero again for the Hammers before five fractious minutes of injury time in which neither side managed to contrive a winner.
Source : PA
Source: PA