Bolton weathered a first-half hammering - including a missed penalty from Carlton Cole - before snatching the lead with a Matthew Upson own goal four minutes after the restart in Saturday's Premier League clash.
Elmander planted a near-post header past Robert Green before West Ham secured a lifeline, when Scott Parker won a second penalty and Mark Noble converted.
But Elmander, who last scored twice in a match in November 2008, wrapped up the points with a low shot past Green after some more slack defending.
Bolton are unbeaten following their opening day draw at Fulham - but West Ham head into daunting games against Manchester United and Chelsea without a point on the board.
Yet, for 45 action-packed minutes it seemed as if the points were destined for Upton Park as the Hammers bombarded the Bolton goal.
But they could not make it count and Bolton punished them ruthlessly.
Kieron Dyer, Pablo Barrera and Frederic Piquionne came into the team and they brought variety and pace to the West Ham attack that was so sorely missing at Aston Villa last weekend.
After an early scare, when Elmander shot wide, West Ham laid siege to the Bolton box.
Scott Parker, Noble and Barrera all fired in shots from distance before Dyer latched on to a clever reverse pass from Piquionne to reach the byline.
Dyer pulled the ball back for Noble - but Stuart Holden had retreated expertly and he intercepted the pass just two yards out from the Bolton goal.
West Ham continued to pile forward. Barrera rifled another shot over the bar before Julien Faubert's volley from the edge of the box flew straight to Jussi Jaaskelainen.
The Hammers attacked with pace and purpose but when Zat Knight failed to deal with Herita Ilunga's low cross, Dyer curled his shot wide.
Gretar Rafn Steinsson was booked after hauling Dyer down on the halfway line as West Ham looked to counter-attack and two minutes later the Bolton full-back conceded a penalty.
Steinsson felled Cole on the edge of the box - but the West Ham striker's side-footed effort was weak and Jaaskelainen saved comfortably to his right.
But Bolton barely had time to catch their breath as West Ham attacked with tempo. Cole sought to make amends immediately but his drilled cross-shot was palmed clear by Jaaskelainen.
Referee Andre Mariner then waved away appeals for a penalty after Cole's clipped cross struck Knight on the hand.
Parker picked out Dyer in the box with a perfectly-weighted pass but Jaaskelainen tipped his shot onto the post.
West Ham had fired in 11 shots without success in the first half - and it took route-one Bolton less then four minutes to make them pay.
Elmander flicked on Jaaskelainen's goal-kick and Upson, under pressure from Davies, stooped to head the ball past Green and into his own net.
To make matters worse for the England defender, he took a boot in the face and was replaced with a bloody nose by Winston Reid.
The New Zealander had an immediate chance to draw West Ham level when Noble's free-kick feel to him in the Bolton box but his downward volley down went straight to Jaaskelainen.
Bolton then had two penalty shouts turned down in the same move. Lee Chung-yong went down in a challenge from Ilunga after cutting in to the box before Parker was struck on the hand - but Bolton soon had their second.
Lee was given all the time he needed to swing the cross in from the right and Elmander planted his near-post header past Green.
West Ham were given a lifeline when Parker was fouled by Gary Cahill as he tried to latch on to a lofted ball into the box and referee Mariner awarded a second penalty.
Noble took over the responsibility from Cole and he buried his strike to bring West Ham back into the game - but not for long.
Any home hopes of a late comeback were wrecked when Ilunga failed to deal with a ball into the West Ham box and Elmander drove his low shot past Green to wrap up the points.