Odemwingie came off the bench after 72 minutes and four minutes later added to the opening goal from Brunt as Albion moved out of the bottom three.
It condemned Wolves to a fifth successive defeat - their worst sequence at the top level since 1984 - and earned the Baggies their first top-flight win over their Black Country rivals for 29 years.
Roy Hodgson also celebrated his first managerial win over his Wolves counterpart Mick McCarthy at the sixth attempt.
Wolves had more of the play during the opening 45 minutes but the home side always looked dangerous on the counter-attack, with Shane Long in particular a constant threat.
After the break Albion took command with Paul Scharner excelling in midfield and Jerome Thomas impressing on the flank.
Wolves were the first to threaten and a cross from Stephen Ward found its way to Jamie O'Hara on the far side of the Albion box, but his left-footed shot was blocked by debutant Billy Jones.
Baggies keeper Ben Foster turned aside a cross-shot from Adam Hammill after he had skipped past the challenge of Jones.
But Albion went ahead through their first meaningful attack via Brunt after eight minutes.
Youssouf Mulumbu picked out the run of the over-lapping Jones and he cut the ball back across the area to Brunt who hammered a rising shot past Wayne Hennessey from 12 yards out.
Wolves retaliated and came close to equalising five minutes later.
Foster blocked Milijas's low drive but the rebound fell to Doyle inside the six yard box who looked certain to tap in only for Albion defender Jonas Olsson to make a superb block tackle.
Wolves defender Christophe Berra became the first player to be booked after 26 minutes after a mis-timed challenge on Long.
Albion were now looking more menacing on the counter-attack.
It needed a fine tackle from Ward to prevent Long doubling their lead after Thomas had sent the ball into the danger area.
Long then burst clear down the left flank before squaring the ball for the recalled Paul Scharner but he needed a second touch and curled his shot past the far post.
Foster was forced to finger-tip a deflected drive from Berra over the bar.
Albion were incensed at the start of the second half when Roger Johnson, Wolves' last defender, appeared to bring down Long only for referee Chris Foy to wave play on.
Replays indicated Johnson had made no contact with the ball.
McCarthy brought on Sylvan Ebanks-Blake for Milijas after 55 minutes - and he almost made an immediate impact.
The striker teed up Hammill whose low drive was finger-tipped by Foster around the far post.
Johnson should have equalised after 67 minutes when he outjumped Jones to get on the end of a Doyle centre but he headed wide from close range.
Odemwingie entered the action with 18 minutes remaining at the expense of Tchoyi.
The Nigeria international quickly made an impact in teeing up Thomas whose low shot was blocked by the feet of Hennessey.
Then after 76 minutes Odemwingie doubled Albion's lead with his second goal of the campaign.
Mulumbu made a probing run before finding Scharner who back-heeled into the path of Odemwingie.
He took one touch before drilling a low shot past Hennessey into the corner of the net.
Odemwingie could have made it 3-0 but shot over with only Hennessey to beat.