Wolves were particularly threatening on the flanks with the pace and direct running of Matthew Jarvis to the fore on the left and the combined efforts of the ever-willing Richard Stearman and David Edwards a constant menace on the right.
Kevin Doyle was just as lively in attack and a fine pass to Sylvan Ebanks-Blake almost led to a second home goal early on.
But while Wolves were undoubtedly the more fluent, Bolton did settle after a chanceless opening 25 minutes and Ivan Klasnic twice had decent shooting opportunities before the break.
The first one was easily dealt with by Marcus Hahnemann but the second he blazed wildly over after a fine run and astute pass by Chung-Yong Lee.
Gary Megson's men upped their game after the break but it was only after Milijas made it 2-0 with a rasping shot from distance that the visitors started to pose a serious threat.
A great last-ditch challenge by home full-back Stephen Ward prevented Tamir Cohen from getting a shot away.
And the lively Matthew Taylor was denied by a smart save by Hahnemann who got down quickly to keep out the former Portsmouth man's low first-time shot.
But Elmander pulled a goal back when sloppy marking at a corner allowed him to score from close range.
McCarthy delighted with 'massive' win
Bolton had their chances to salvage a draw late on with Klasnic shooting tamely at Hahnemann and Wolves somehow surviving an almighty late scramble.
Wolves boss Mick McCarthy: "For an hour and 15 minutes I thought we were terrific.
"We started great and kicked on. The goal was offside but it was my turn for a bit of luck.
"We got involved in a scrap after they scored but I thought we defended them really well. As soon as they get one they were lifted but that game should have been over long before they scored the goal."
Bolton manager Gary Megson: "We have spoken about this before the game and talked about the fact that nine of their 11 goals have come from set-pieces so it's soul-destroying when they score after three minutes from a set-piece.
"Defending that first set-piece we were poor but nowhere near as poor as the linesman. It was a poor, poor decision.
"In the last 20 minutes you've seen the away team take the game to the home team. We created a lot of problems, created a lot of chances and they couldn't get out of their half yet we left it too late."
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