PABLO Ibanez came to Albion's rescue as his first-ever Barclays Premier League goal saw them bounce back from two successive defeats with a precious away point.
The Upton Park clash started well for the Baggies, who took a 38th-minute lead thanks to top-scorer Peter Odemwingie's fifth goal of the campaign from the spot.
But the visitors shot themselves in the foot either side of the break as defensive errors led to Scott Parker levelling two minutes before the break and Frederic Piquionne firing the Hammers ahead with a 50th-minute penalty.
However, Roberto Di Matteo's troops refused to throw in the towel and Ibanez enjoyed another East End knees up by following up his crucial Carling Cup strike at nearby Leyton Orient with a 71st-minute equaliser.
Heavy London traffic meant the Baggies did not arrive at the stadium until an hour before kick-off, when they revealed four changes - two enforced.
James Morrison (knee) and Steven Reid (Achilles) returned after injury in place of benched duo Simon Cox and Nicky Shorey, who was carrying an ankle problem.
Graham Dorrans was recalled in place of the suspended Youssouf Mulumbu and Odemwingie was preferred to Marc-Antoine Fortuné, who was relegated to substitute, up front.
The first effort of the game came in the ninth minute when Morrison threaded the ball through to Odemwingie on the right-hand edge of the penalty area and the Nigeria striker got a low shot away that Robert Green dealt with comfortably.
The visitors were presented with a golden opportunity to open the scoring two minutes later as they broke from a Hammers corner.
Scott Carson found Chris Brunt and he set Jerome Thomas on his way down the centre.
But with Dorrans and Odemwingie in space in the box either side of him, the ex-Charlton ace chose to shoot and could only muster a tame 18-yard effort straight at Green.
Albion gave the ball away in midfield in the 20th minute and Pablo Barrera pounced before playing it over the top for Carlton Cole, who cut inside Reid and fired a 20-yard shot wide of the left-hand post.
Six minutes later, Ibanez stole in on a Brunt free-kick and headed high and wide when he should at least have hit the target from 12 yards.
At the other end, Cole went closer as he checked his run in the box from Barrera's right-wing corner and nodded inches over the bar.
Another breakout by the Baggies on 35 saw Odemwingie attack the United back four, but his attempt to slip Thomas in on goal gave the former Arsenal winger too much to do.
Brunt's inswinging free-kick in the 37th minute crept through the crowd of players in the box and forced Green into a last-ditch parry, with Odemwingie lurking.
Gabriel Tamas' follow-up shot was deflected behind and from the resultant Brunt corner referee Mike Dean spotted a push on Reid by Luis Boa Morte in the box and awarded a penalty.
Top scorer Odemwingie stepped up and coolly slotted the spot-kick in the bottom right-hand corner to take his season's tally to five and give the Baggies a 38th-minute advantage.
But the visitors' lead was short-lived.
Paul Scharner was caught in possession by Cole and he exchanged passes with Dyer.
Although Scharner recovered to dispossess the Hammers striker, the ball ran to Scott Parker, who fired a 25-yard exocet into the top left-hand corner of the net to level two minutes before the break.
Thomas teed up Brunt at the opposite end shortly afterwards - but the Northern Ireland international dragged his effort wide from the edge of the area.
In the closing seconds of the half, Boa Morte wriggled free of Morrison on the left-hand side of the area before forcing a near-post save from Carson with a powerful 15-yard drive.
Four minutes into the second half, Albion again shot themselves in the foot when Tamas was deemed to have pushed Dyer in the box and Wirral official Dean awarded his second penalty of the game.
Piquionne smashed home the spot-kick to give West Ham a 50th-minute lead.
Two minutes later, Reid's strong run down the right saw him feed Odemwingie who flashed a dangerous ball across the face of goal.
It was then the hosts' turn as Dyer again cut inside from the right and saw his powerful goalbound drive bravely blocked by Tamas.
Avram Grant made a tactical change on 54 as Radoslav Kovac came on for Boa Morte.
Ibanez gifted possession to Barrera on 62 and he found Dyer on the edge of the area whose neat flick presented Piquionne with a sight of goal.
The former Portsmouth striker took aim but saw his low strike fly inches past the far post, with Carson beaten.
Di Matteo made a change in the 67th minute as Simon Cox came on for Dorrans.
And the former Swindon hot-shot was straight in the action.
Morrison teed him up and he fired inches past the right-hand post from 20 yards.
Odemwingie chested down Reid's throw-in on 69 and turned sharply before seeing his rising drive clutched by Green.
West Ham cleared Brunt's left-wing corner in the 71st minute but Morrison played it back out to the same man and he delivered a pin-point cross to the back post for Ibanez to power home a header for the equaliser.
Two minutes from time, Daniel Gabbidon was lucky to stay on the pitch as he prevented Odemwingie from going through on goal by tugging him back.
Albion finished the game well on top, winning a string of corners and having a late shout for penalty for a foul by Herita Ilunga on Fortuné turned away.
But they could not find the winning goal they probably just about deserved.
WEST HAM (4-3-3): Green; Jacobsen, Gabbidon, Upson, Ilunga; Dyer, Parker, Boa Morte (Kovac 54); Piquionne, Cole (Obinna 76), Barrera (McCarthy 88). Subs not used: Stech (gk), W Reid, Tomkins, Spector.
ALBION (4-2-3-1): Carson; S Reid, Ibanez, Tamas, Cech; Scharner, Dorrans (Cox 67); Brunt, Morrison, Thomas (Barnes 75); Odemwingie (Fortuné 88). Subs not used: Myhill (gk), Tchoyi, Shorey, Zuiverloon.
GOALS: WEST HAM - Parker (43), Piquionne (pen 50). ALBION - Odemwingie (pen 38), Ibanez (71).
BOOKINGS: WEST HAM - Boa Morte (foul 37), Kovac (foul 73), Gabbidon (foul 88).
REFEREE: M Dean (Wirral).
ALBION STARMAN: James Morrison.
PIC: IBANE-T!..Pablo celebrates his equaliser with Gabriel Tamas