Jamie Mackie's 28th-minute strike put the visitors in front before Garry Thompson drew them level.
Argyle goalkeeper David Stockdale made an excellent save to deny Thompson a second before the break, but just after the hour mark Woolford got into the area and his shot was deflected in.
The result leaves the Pilgrims seven points adrift of safety with games rapidly beginning to run out.
But manager Paul Mariner is not yet ready to throw in the towel.
"We are a resilient lot and we will pick ourselves back up from this disappointment," he said.
"I thought we played some good football in the early stages and were the better team for the first half-hour.
"We scored a terrific goal to go in front through Jamie Mackie but for me the turning point came when we lost Richard Eckersley injury.
"It was a bad challenge on him, one which was deserving of a yellow card.
"He will go to hospital for an X-ray on what we fear might be a broken ankle.
"That's another defensive problem for us, we just don't seem to have any luck in that department this season."
Scunthorpe manager Nigel Adkins was all smiles at the end after his side ended a run of three successive away defeats.
"This was a victory we badly needed and I think we thoroughly deserved," he said.
"Even without Gary Hooper we created a lot of chances and it was their goalkeeper David Stockdale who was man of the match with some fantastic saves.
"There has always been total belief in our dressing room that we can succeed this season.
"There was a nervousness out there which I am sure there will be from now until the end of the season.
"But our home form has been good all season and this is where we can achieve what we expect to achieve this season."