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.
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.
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.
