Central defender Collins headed home an 83rd minute cross from Matt Jarvis to move Wolves within a point of the play-offs.
But Wolves, who won for only the second time in eight home games, had to do it the hard way against the relegation-threatened Iron.
Scunthorpe, without an away win since Boxing Day, made the perfect start when Andy Butler's second goal of the season gave them a fifth minute lead.
But that was one of the few times they threatened and their resistance was finally broken 12 minutes into the second half by the unlikely figure of Michael Gray.
Gray, who has never been a prolific goalscorer in his long career, scored his second goal in two games when his 25-yard drive was deflected past Joe Murphy after Scunthorpe had failed to fully clear a cross from Jarvis.
That set up a furious late assault on the Scunthorpe goal with Sylvan Ebanks-Blake crashing a volley against the bar and then seeing his header cleared off the line by Ian Baraclough.
Scunthorpe, who are six points from safety, looked set to ride their luck and pick up a point before Collins broke their resistance.
It was rough on battling Scunthorpe who caught Wolves cold when Gavin McCann's corner was met by the unmarked Butler, whose powerful header from eight yards gave goalkeeper Wayne Hennessey no chance.
It was a setback that Wolves struggled to come to terms with, but they still had enough chances to have at least been on level terms by half-time.
But some poor finishing and a smart save by Murphy frustrated them.
Andy Keogh completely missed a cross from Gray on the half hour and then two minutes later Ebanks-Blake slammed his shot into Gray from just eight yards.
Ebanks-Blake wasted another glorious chance in the 41st minute after being released by Jarvis.
He only had Murphy to beat but the Republic of Ireland international keeper spread himself to beat away a low shot.