Brian Deane's superb strike in the 68th minute had looked like giving Alan Pardew his second successive victory but the Baggies were gifted a point when Hayden Mullins cruelly headed a tame-looking cross past David James and into his own net with just 10 minutes remaining.
It could be argued that the hosts deserved at least a draw after enjoying the greater possession and attacking play overall but that will be of no consolation to the Hammers boss, who almost pulled off a smash-and-grab victory after setting his stall out to deny Gary Megson's team space and hit them on the counter-attack.
Fielding a 5-3-2 formation that saw David Connolly drop in behind strikers Deane and Marlon Harewood and Robbie Stockdale come in for Kevin Horlock in a wing-back role, with Tomas Repka reverting to a back three alongside Christian Dailly and Ian Pearce, Pardew certainly wasn't going to accept a repeat of last month's humiliating 4-3 defeat against Albion.
In complete contrast to that action-packed afternoon, today's first half was a fairly tepid affair, generally dominated by the hosts but without the Hammers being in any real danger. Restricted to a handful of long-range efforts that were comfortably held by James, the Baggies grew more frustrated as the game wore on.
Hammers came out for the second half in clearly more determined mood and slowly but surely began to push their opponents on the back foot. Harewood - who endured a difficult afternoon having suffered with a cold this week - missed a good chance to open the scoring when he completely mis-kicked a Quinn cross, while Connolly wasted an even greater opportunity in the 64th minute, scooping the ball high over the bar after Quinn's long throw had dropped to him just six yards out.
Four minutes later, though, the breakthrough finally arrived. After Harewood's mazy run had been thwarted on the edge of the box, the Albion defence seemed to freeze in anticipation of a free-kick being awarded but were left hopeless as Deane curled in a stunning left-foot shot from the edge the area that gave Hoult no chance.
With striker Danny Dichio having left the field through injury before half-time, the hosts appeared to lack any kind of punch in attack and were again resorting to hopeful efforts from outside the box. Neil Clement's scorcher from 30 yards gave Hammers a fright but it seemed likely they would hold on for an impressive victory.
That was until the 79th minute, when substitute Scott Dobie skipped down the right and clipped in a cross that looked harmless enough until Mullins, stretching to clear, only succeeded in looping the ball over the outstretched arm of James and into the far corner of the net.
With their tails up going into the closing stages, Albion looked capable of completing another heart-breaking comeback but, all credit to the Hammers, they defended with solidarity and ensured that the seven-point gap between the two sides didn't stretch to 10.
With home games against Stoke City and Sunderland to look forward to this coming week, Hammers will be hoping that the difference is even closer this time next week.