The Serbia international midfielder opened his account for the club following his £2.6million summer move from Red Star Belgrade with an unstoppable 30-yard drive in the 63rd minute.
It clinched a first win in nine games for Wolves who had made a dream start when Jody Craddock gave them the lead after just 122 seconds.
The victory saw them leapfrog over Bolton - whose winless run has now stretched to five games - and move within a point of safety.
Gary Megson's struggling side badly missed suspended striker Kevin Davies as they carried little threat in attack until the closing stages despite the best efforts of Ivan Klasnic.
Bolton did give themselves hope of producing a dramatic finale when substitute Johan Elmander struck 11 minutes from time. But anything other than a win would have been rough on Wolves who dominated affairs as they sparked fresh life into their battle for survival.
Having been caught cold themselves after just 125 seconds against Birmingham City in their previous match, Wolves ensured they were first out of the blocks against Bolton.
After Kevin Doyle had been fouled, Milijas whipped in a free-kick that Christophe Berra headed goalwards before Craddock volleyed the ball past Jussi Jaaskelainen from seven yards.
Wolves should really have gone on to make the game safe before half-time but were unable to turn their domination into further goals.
Sylvan Ebanks-Blake had a close-range shot deflected wide by Gary Cahill, Kevin Doyle saw his header deflected over the bar and Jaaskelainen then held on to a fierce volley from Milijas.
Bolton did threaten briefly at the start of the second half, when Cahill's 54th-minute flick from Chung-Yong Lee's corner flashed just wide.
But their comeback hopes were effectively dashed when Doyle dispossessed Gavin McCann and the loose ball ran into the path of Milijas who let fly with a drive that whistled past the right hand of Jaaskelainen.
It should have been the signal for Wolves to cruise to victory but Elmander's goal changed all that. He bundled the ball home through a crowded goalmouth after Tamir Cohen had nodded down a Matt Taylor corner.
It sparked a frantic late rally from Bolton with Klasnic being denied an equaliser thanks to a smart save from Marcus Hahnemann.