Owen Coyle’s side moved into fifth place in the Premier League thanks to a combination of clinical finishing by Matt Taylor and Elmander and some wayward shooting from Albion at the Reebok Stadium.
Bolton were later surpassed by Tottenham after the north London club overcame having a man sent off to win at Aston Villa later on Sunday but regardless of that result, Wanderers will be firmly in the running for a Europa League spot if they maintain this form.
They have now won four of their last seven league matches after riding their luck against the Baggies.
Albion’s top scorer Peter Odemwingie was fit to start after recovering from a calf injury, while midfielder Youssouf Mulumbu returned from suspension.
Albion midfielder Graham Dorrans had an early sight of goal when he fired straight at Jussi Jaaskelainen.
Bolton responded and Elmander drove over the bar from a good position.
But West Brom were looking more dangerous and Somen Tchoyi sent another effort wide before Odemwingie beat the offside trap, collected James Morrison’s pass and shot wide.
Those missed chances proved costly as Taylor gave Bolton the lead in the 40th minute.
Taylor’s pass found Lee Chung-Yong and the South Korean went round Albion keeper Scott Carson before playing in Taylor, who calmly slotted home his first goal of the season.
West Brom sought an immediate leveller and Gonzalo Jara forced Jaaskelainen
to tip a shot over his crossbar.
Roberto Di Matteo’s side launched a sustained assault on the Bolton goal in the second half and Tchoyi led the way as he tested Jaaskelainen from a tight angle.
Tchoyi was involved again as he whipped in a cross that Chris Brunt got to ahead of Jaaskelainen, only for his header to cannon back off the post before being hacked away.
Odemwingie should have equalised when he found himself with only Jaaskelainen to beat but his effort was just wide of the post.
Di Matteo sent Ishmael Miller on for Morrison, and the striker almost had an immediate impact only for Gary Cahill to somehow get in the way of his goalbound shot.
But Bolton finished strongly and Scott Carson had to make a fine stop to keep out Stuart Holden’s free-kick.
Coyle’s men finally wrapped up the points in the 86th minute. Elmander tried to play in Ivan Klasnic and, when the ball came back to him, the Swede slotted under Carson from the tightest of angles.