Martin Petrov's first-half penalty and a 70th-minute own goal from Billy Jones looked likely to send Coyle's Trotters into next week's final-day decider at Stoke with their top-flight destiny in their own hands.
But the Baggies emphatically proved there is life after Roy Hodgson as Chris Brunt reduced the deficit two minutes after Jones's mishap, then Morrison converted a cross from fellow substitute Simon Cox with seconds to spare.
Nerves had been evident in the early stages but the home side started like they were focused on the job in hand, Chris Eagles lashing a long-range shot into the side-netting with less than two minutes on the clock.
Albion immediately responded with a chance of their own, Liam Ridgewell flicking in a cross from the left and Marc-Antoine Fortune connecting with a flicked header which was gathered by Adam Bogdan in the Bolton goal.
Bolton should have gone ahead in the 11th minute when Petrov fired a cross from the left that eluded everyone except Kevin Davies, who stole into the six-yard box only to blaze his shot high over the bar.
With Bolton's nerves at the back plain to see, the Baggies carved out a succession of chances with Gareth McAuley and Fortune both coming close before Fortune played Brunt into the box only for the striker to side-foot wide.
And Albion came closer still in the 19th minute when the dangerous Fortune was allowed to feed Long in the Bolton box and the striker turned David Wheater before jabbing his shot against Bogdan's left-hand post.
Foster tipped a David Ngog header over the bar in the 21st minute and two minutes later Bolton grabbed the lead from the penalty spot, Petrov slotting home after Youssouf Mulumbu fouled Mark Davies in the box.
Petrov's spot-kick clearly settled Bolton's nerves and the home side went on to enjoy their most dominant spell without creating any more clear-cut chances, while Keith Andrews prodded a half-chance straight at Bogdan for the Baggies.
Eagles came close to extending Bolton's lead five minutes from the break when he drilling a rising shot just over the after a sustained period of pressure around the West Brom box.
Albion almost created a chance seven minutes into the second half when Brunt's neat through-ball played in Long, but as Tim Ream jumped in with a superb saving challenge, the near-side linesman belatedly flagged for offside.
Albion came close again in the 58th minute when Brunt shot straight at Bogdan from a Ridgewell cross from the left, and moments later a header from Jonas Olsson was also well held by the goalkeeper.
Eagles came close on the hour with a blazing shot across the face of goal and Ngog should have done better with a chance created for him by Nigel Reo-Coker in the 65th minute, but his hesitation allowed Andrews to nick the ball off his toes.
The Baggies still carried a threat and Ridgewell almost caught the Bolton back-line unawares in the 68th minute when he stole into the left side of the area and drove a shot straight at Bogdan from a tight angle.
Foster denied Kevin Davies in the 71st minute with a brilliant reflex save, getting down to scoop the ball off the line after the striker got his head to a Petrov cross.
But Bolton grabbed their second one minute later in bizarre fashion, when Ridgewell's attempted clearance from another Petrov cross struck team-mate Billy Jones in the chest, and ricocheted into the net past a helpless Foster.
With Bolton's fans still prematurely celebrating survival, Albion reduced the deficit a minute later when Long was given space on the right side of the box and cut the ball back for Brunt to strike low past Bogdan.
And with the final 20 seconds showing on the Reebok Stadium clock, Cox hooked a ball into the box for fellow substitute Morrison to lash home at the far post and claim a dramatic - and, for Bolton, potentially fatal, point.