The Baggies poured forward in search of an equaliser, with Odemwingie blazing wide from a promising position on the right.
Martin Petrov wasted a clear chance for Bolton and Odemwingie slashed wide with an effort late on in the game.
Coyle claimed Baggies striker Peter Odemwingie should have been flagged offside before he crossed for James Morrison to level the match.
But West Brom equalised 12 minutes from time when a cross from the lively Peter Odemwingie was nodded home by Morrison.
They started with a bang as Peter Odemwingie forced a save from the Belgian keeper in the opening minute of the game.
Moments later, a delicious right-wing cross from Morrison found Odemwingie bursting between two defenders, but the frontman's header sailed over the bar.
But Albion's pressure deserved a goal and top scorer Odemwingie duly obliged.
Robin van Persie nodded against the bar before a horrendous mix-up between Manuel Almunia and Sebastien Squillaci gave Peter Odemwingie a simple finish.
"The disappointment for me is that with the goal they scored, Odemwingie is clearly offside when the ball is played through, " Coyle said.
Substitute Matt Taylor went close for Bolton before Odemwingie sliced horribly wide after a long ball had given him a clear sight of glory.
With the home side firmly on the front foot, Odemwingie began to show why he was named September's Premier League player of the month.
Having hit the side-netting from Mulumbu's clever ball over the top moments earlier, Odemwingie reaped maximum advantage from Sylvain Distin's misreading of Brunt's lobbed pass.
Peter Odemwingie, Gonzalo Jara and Jerome Thomas put Albion 3-0 up before Samir Nasri gave the Gunners a glimmer of hope after scoring a late double.
Almunia conceded a first-half penalty for bringing down Odemwingie and, although he saved Brunt's resulting spot-kick, he was later beaten at his near post by Jara.
Osaze Odemwingie struck either side of halftime break for Nigeria at the Tundavala Stadium in Lubango before substitute Obafemi Martins sealed victory for the the 'Super Eagles'.
The Baggies came close when Gretar Steinsson headed a whipped cross just over his own bar, and again when Odemwingie's lay-off played in Morrison, who fired past the post.
Predictably, the home response was led by the irrepressible Odemwingie, who had already missed an opportunity to score for the sixth successive game when he set up the Baggies' decisive goal.
In a gripping finale, Piquionne blazed over and Odemwingie missed two decent chances to win the contest, ensuring West Ham climb off the foot of the table with this well-earned point.
Green kept West Ham in the match with an excellent save to his left after Odemwingie skipped away from two challenges before attempting to curl in from the edge of the box.
Shuaibu Amodu's side doubled their lead two minutes after the break when the unmarked Odemwingie was able to control a cross from Yakubu Aiyegbeni and tap the ball home from close range.
Morrison should have made it 3-1 moments later, but Kingson saved with his legs to atone for his earlier error and the Ghanaian international keeper then closed down Odemwingie and pulled off another fine stop.
Peter Odemwingie sent a shot bouncing wide with Hart scrambling across his goal and, after Brunt blasted over, substitute Fortune fired into the side-netting after running clear and Carlos Vela headed wide when well placed.
First Stockdale saved from Peter Odemwingie's low snap-shot before a through ball from Chris Brunt split the Fulham defence and found Jerome Thomas who went one-on-one with Stockdale but the keeper stood firm and saved well.
But West Brom were rampant and their lead should have been stretched to three when Peter Odemwingie escaped the attention of Wayne Bridge from Mark Noble's corner, but could only find Green with his close-range header.
The goal seemed to take the stuffing out of Spurs, who failed to engineer another chance of note - in fact it was Odemwingie who came closest to grabbing a winner as his low drive fizzed narrowly wide.
Such adventure, combined with West Brom's pace on the counter-attack, ensured a lively afternoon for Everton keeper Tim Howard, who acrobatically palmed over a Brunt free-kick and somehow managed to get a hand to a close-range header from Odemwingie.
West Brom boss Roberto Di Matteo said he had not seen a replay of the Odemwingie incident but declared himself satisfied with a point which stretched his side's unbeaten home run to 14 league games and kept them in sixth place.
While Nigeria's performances at the Africa Cup of Nations in Angola were lacklustre, there is no denying that players such as Chinedu Obasi, John Obi Mikel and Osaze Odemwingie have the potential to make the same kind of impact on the world stage as some of their illustrious Nigerian predecessors.
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