Wanderers took the lead in the 10th minute thanks to Matt Jarvis, who volleyed home after Robert Green had failed to clear a cross.
But Noble made no mistake from the spot in the 53rd minute, lashing the ball past Marcus Hahnemann.
A point each means Wolves remain in 19th place in the table with West Ham below them at the bottom of the pile.
Both sides went into the match knowing a win would lift them out of the relegation zone and it was the hosts, without a win in six league fixtures, who made the more positive start.
There was an initial setback when Jody Craddock - named captain in place of the suspended Karl Henry - had to come off only five minutes into the game, with Richard Stearman introduced as a substitute and Christophe Berra taking the skipper's armband.
David Edwards saw a shot deflect wide soon after though, and Green could only punch the resulting corner to David Jones, whose effort was off target.
Moments later Green fisted the ball away again from Stephen Ward's cross, and this time Jarvis was able to capitalise, volleying home to put Wolves in front.
The England goalkeeper, whose form has fluctuated this season, then did much better to tip away a strike from Jones.
Wanderers looked as if they had a second goal in them and it might have come if a golden shirt had been on the end of Kevin Doyle's ball across the box, but instead it was Tal Ben Haim who diverted it behind for a corner.
Steven Fletcher headed the ball back into the danger zone where Green managed to beat the rising Stearman.
Manuel Da Costa then made what could have been a costly error by slipping on the edge of his own area, but having picked up possession, Wolves were unable to make the most of it, with Jarvis' shot rebounding off Danny Gabbidon and leaving the Hammers defender on the turf.
Having struggled to make an impression in the opening period, West Ham were given a lifeline at the start of the second half when Kevin Foley bundled over Victor Obinna in the box and referee Mark Clattenburg pointed to the spot.
Noble stepped up and drew things level with a confident conversion that sent Hahnemann the wrong way.
Within seconds Wolves were back on the attack and Green made another wild-looking punch, Jones drilling the ball back towards goal but seeing the attempt blocked.
The visitors then almost turned the game on its head as Frederic Piquionne rifled against the crossbar.
At the other end Jarvis appealed in vain for handball after his cross hit Lars Jacobsen and Stearman headed a corner wide.
Play switched again and Kieron Dyer twisted and turned in the box before unleashing a strike which fell to Obinna, whose shot was also diverted away.
Wolves boss Mick McCarthy withdrew Fletcher for Jelle Van Damme, while Avram Grant brought Carlton Cole into the fray for West Ham in place of Dyer.
Cole was not quite quick enough to latch onto a neat pass from Noble soon after and then lost control of the ball as he advanced on goal with a little under five minutes remaining.
McCarthy threw on another striker in Sylvan Ebanks-Blake but it was Piquionne who had the ball in the net at the death, only for Clattenburg to disallow the effort for handball and show the striker a yellow card.