Martin Petrov's first-half penalty and an own goal by Billy Jones with a quarter of an hour left looked to have given Owen Coyle's men all three points, but Chris Brunt's goal immediately after the restart set up a frantic finale.
Bolton looked like having done enough to hold off a late onslaught by Roy Hodgson's men, but James Morrison volleyed home at the far post in the final minute to give the new England manager's side a share of the points.
The result was no less than West Brom deserved for being the better side for much of the game, while results elsewhere went against Bolton, meaning the Trotters now need both a win against Stoke and a series of favours from other clubs if they are to remain in the top flight.
Bolton came into the match desperate for three points to try and pull them out of the bottom three and they started brightly, coming close to an opening goal after just 10 minutes as Petrov's stinging shot from the left corner of the box forced a diving, one-handed save from Ben Foster.
And Bolton had another gilt-edged chance just two minutes later as Petrov's ball across the box was nodded down by Nigel Reo-Coker towards Kevin Davies at the far post, but the veteran striker was furious at himself for skying the ball over from just four yards out.
Kevin Davies made a similar error from an almost identical build-up just three minutes later as Bolton continued their early assault on the West Brom goal, this time scarcely making contact with the ball as he guided it off the pitch.
West Brom had plenty of early chances too, however, with the end-to-end game being played at breakneck speed. Just after the first of Kevin Davies's misses Liam Ridgewell forced Adam Bogdan into a brilliant reaction save, the Bolton keeper getting down and to his left to stop certain goal.
And on 20 minutes West Brom were just inches away from scoring as Shane Long's brilliant turn and shot under pressure was only stopped by Bogdan desperately shinning the ball onto the left post.
West Brom had gradually begun to take charge when Bolton took the lead, however: Youssouf Mulumbu and Keith Andrews combined to needlessly bundle Mark Davies over in the box, leaving referee Kevin Friend no option but to point at the spot.
Foster guessed correctly with his early dive for the spot kick, but such was the power in Petrov's shot that the ball found the net anyway.
Both sides could have scored again before the break, with an unchecked Chris Eagles firing over from the edge of the box, while West Brom came within an ace of an equaliser as Marc-Antoine Fortune shot over after Bogdan fumbled.
The second half began in more cagey fashion, with both sides looking as if they had been given a dressing down at half-time for some of the slack defending on show.
West Brom came close to finding an equaliser just before the hour mark when Graham Dorrans's first-time shot from the edge of the box forced another good stop from Bogdan, while eight minutes later Ridgewell was denied by Bogdan at the near post.
With 20 minutes left to go, however, Bolton appeared to have wrapped up the points as a magnificent break down the left by Petrov cut the Baggies defence open.
The chance initially appeared to have been lost when Petrov's ball missed both Kevin Davies and sub Ivan Klasnic. The unfortunate Ridgewell cleared the ball straight into team-mate Jones, who deflected it straight over Foster and in to make it 2-0.
The home fans began their celebrations in earnest, only to have them silenced five minutes later when a lovely run by Long ended in a pass that was blocked and fell straight to Brunt, who slammed the ball home with a left-foot strike.
From then on West Brom laid siege to the Bolton goal, with Simon Cox's roundhouse effort almost beating Bogdan.
And despite Bolton having 11 men behind the ball, West Brom found an equaliser as Jones and Brunt combined on the right, with Brunt then passing across to the far post where Morrison was there to volley into the roof of the net.
Bolton's hearts were broken, and though Dedryck Boyata had a great chance in the seventh minute of injury time he could only succeed in blazing the ball out for a goal kick.
The point leaves Bolton stuck in the bottom three and two points adrift of Wigan and QPR, while West Brom are closing in on securing a top 10 finish to - their best-ever in the Premier League - that would end Hodgson's tenure on a high note.