Kenny Jackett's men took an army of 8,880 fans to Stadium MK and the travelling hordes were rewarded with a late winner from substitute Liam McAlinden.
The striker's 81st-minute header came just two minutes after the hosts had been reduced to 10 men following Sanmi Odelusi's dismissal for two yellow cards.
Brentford's goalless draw at Oldham Athletic added to Wolves' joy as Jackett's side edged closer to an immediate Championship return.
Oldham produced a solid rearguard display to frustrate their high-flying visitors and secure a crucial point in their survival bid.
Fortunately for Brentford, third-place Leyton Orient's poor form continued as Russell Slade's side slumped to a 1-0 home loss against mid-table Bradford City.
Aaron McLean netted the only goal of the game to make it four without a win for Orient, who are now four points behind Brentford having played two extra games.
The sides immediately behind Orient kept up the pressure, with both Rotherham United and Preston North End still very much in the hunt for automatic promotion.
Rotherham made it 15 league matches unbeaten with a 2-1 triumph over Bristol City, inspired by James Tavernier's double, while Preston were indebted to Joe Garner for his 13th-minute winner at home to Crawley Town.
At the other end of the table, Notts County took a leap towards safety as they moved out of the relegation places thanks to a 2-0 home win against Colchester United.
Crewe Alexandra replaced them in the drop zone after they were beaten 2-1 at home by Coventry City.
Elsewhere, Stevenage drew 1-1 with Port Vale, Walsall beat Shrewsbury Town 1-0 in a match that saw both sides finish with 10 men, Swindon Town boosted their play-off hopes with a 2-1 win over Sheffield United, and Tranmere Rovers were held to a 0-0 draw at home by Carlisle United.
