Elmander, put home his fourth of the season midway through the second half to give Bolton the lead at the Hawthorns, only for James Morrison to score a late equaliser to even the tie at 1-1.
Morrison struck with 12 minutes to play and rescue a point which leaves the Baggies, promoted from the Championship last season, in a creditable sixth place, while Bolton sits in mid-table after drawing five of the first seven matches.
The hosts carved out the first opportunity of the game in the second minute with Morrison just unable to get on the end of Chris Brunt’s cross.
Soon after that, Bolton captain Kevin Davies had a sight of goal but he couldn’t get any real power on his header from Lee Chung-Yong’s cross.
Gary Cahill, back in the Bolton team after serving a three-match suspension, made a better connection with Martin Petrov’s corner but the England defender’s header went narrowly over the bar.
West Brom striker Peter Odemwingie, named as the Premier League’s player of the month for September, drilled a low shot off-target as he looked to add to his tally of three goals in five games since joining Albion in August.
Bolton started the second half in purposeful fashion and after Scott Carson had tipped away an effort from Petrov, Cahill saw his header cleared off the line.
Owen Coyle’s team were rewarded for their pressure in the 64th minute as Davies laid the ball into the path of Swedish forward Elmander, who broke into the box and slotted home his fourth goal of the season.
Odemwingie had a great chance to equalise after as he pounced on an error by Zat Knight, but he dragged his shot wide.
The Nigerian made amends though as he curled over a wonderful 78th minute cross and Morrison rose highest to power home his headed equaliser.
Odemwingie created another opportunity by squaring to Brunt, but the midfielder was denied by a brilliant save from Jussi Jaaskelainen.