Premier League - Long header sinks Bolton
But West Brom were rewarded for their second half dominance when Long, returning from injury, leaped high to power a brilliant header into the bottom corner to secure all three points.
The defeat will heap the pressure back on Coyle who, after the brief respite following his side's 5-0 win over Stoke, has guided Bolton to just nine points of a possible 36 this season.
But there was little between the sides in a combative, yet often exciting, first half.
The Trotters enjoyed the better of the early exchanges but it was the home side that took the lead when Thomas collected a neat through ball from Zoltan Gera before assuredly taking the ball around Jaaskelainen and tapping in his first goal since February.
But Thomas's afternoon took a turn for the worse when he tangled with Muamba in the box to concede a penalty, allowing Klasnic to calmly slot the ball beyond Ben Foster to level the game.
While remaining a tight match, it became a scrappier affair after Klasnic's goal, with the best chance falling to Bolton's Mark Davies.
Davies exchanged a neat one-two with Klasnic on the edge of the box before beating two players and firing a left-footed effort at goal, forcing a crucial save from Ben Foster.
The second half lacked the intensity of the first, but West Brom applied several minutes of sustained pressure on the Bolton goal after the break.
Roy Hodgson's side started to focus their attacks down the Bolton right and were rewarded 11 minutes into the second period when left-back Nicky Shorey clipped a cross to Long, who leaped above David Wheater to plant a brilliant header into the bottom corner.
Bolton didn't turn up for the second half and West Brom should have killed off the game but Long, Thomas and James Morrison were all guilty of misses.
But there was no grandstand finish as Bolton, despite a host of second half changes, failed to create enough chances to justify taking away a point.