Owen Coyle’s team won for the first time this season as Matthew Upson’s own goal and an Elmander strike put the visitors in control after Carlton Cole’s first half penalty was saved by Bolton goalkeeper Jussi Jaaskelainen.
Mark Noble got one back for Avram Grant’s team from the spot but Elmander struck again to put the result beyond doubt.
This was another dispiriting result for the Hammers, who had been easily beaten 3-0 at Aston Villa last weekend, and once again failed to convince.
Kieron Dyer made only his eighth Premier League start in three years as Grant rang the changes following the Villa defeat.
Grant also gave Mexican winger Pablo Barrera and French striker Frederic Piquionne their first starts.
Bolton had an early chance when Stuart Holden intercepted Noble’s pass and fed Kevin Davies, who held off Danny Gabbidon to tee up Elmander, but his low shot flashed wide.
Dyer, whose last full game for West Ham was his club debut in 2007, had a sight of goal when Bolton defender Zat Knight failed to deal with Herita Ilunga’s low cross, but he shot wide from a good position.
Grant’s team should have taken the lead in the 32nd minute when Gretar Steinsson gave away a penalty by chopping down Cole.
But Cole’s spot-kick was weak and Jaaskelainen went the right way to save comfortably.
Cole tried to make amends immediately but his drilled cross-shot was palmed clear by Jaaskelainen.
Scott Parker picked out Dyer in the box with a perfectly-weighted pass but Jaaskelainen tipped his shot onto a post.
Bolton emerged with a more determined approach after half-time and took the lead in the 48th minute when Elmander flicked on Jaaskelainen’s goal-kick and Upson, under pressure from Davies, stooped to head the ball into his own net.
New Zealand defender Winston Reid, on for the injured Upson, had a chance to draw West Ham level when Noble’s free-kick fell to him in the Bolton box, but he couldn’t beat Jaaskelainen.
Bolton punished the hosts immediately as Elmander planted a near-post header past Robert Green in the 68th minute.
West Ham were given a lifeline when Parker was fouled by Gary Cahill in the 79th minute and Noble drove home the resulting penalty.
But any hopes of a late comeback were wrecked when Ilunga failed to deal with a cross in the 84th minute and Elmander drove his low shot past Green.