The 24-year-old scored twice in the second half to hit the Magpies with their second consecutive league defeat.
Kevin Nolan seemed to have brought the game to life when cancelling out Woolford's opener just after the hour mark.
But the Iron's frontman struck again with 10-minutes left on the clock to see out a 2-1 win at Glanford Park.
Newcastle stay in second place despite defeat but now stand without a win in their last four games.
ChancesWith Geremi and Jonas Gutierrez back in their starting line-up after surrendering top spot with defeat at Nottingham Forest on Saturday, Newcastle could have been two goals ahead inside the opening 10 minutes were it not for the brilliance of Joe Murphy in the Scunthorpe goal.
Both chances fell to Nolan and both were made by Jose Enrique.
The first opportunity saw Nolan power a header towards the top corner that Murphy did brilliantly well to turn away, before he reacted even quicker to change direction and push Nolan's improvised back-flick clear.
At that point it looked as though it was only a matter of time before Newcastle scored, but Scunthorpe managed to get a foothold on the game and were unfortunate not to go into the half-time break ahead.
Gary Hooper wasted their first chance when he blazed over from six yards with a near open goal at his mercy after Marcus Williams' fizzing cross.
Paul Hayes then scuffed a drive wide when he should have tested Steve Harper, before the Newcastle goalkeeper was made to work as he saved at the feet of Hooper who was sent racing clear by Grant McCann.
Newcastle continued to create chances of their own too, with Nolan firing over when well set after a Gutierrez centre, while Andy Carroll forced Murphy into another fine save with a low drive.
The chance of the opening half fell to Scunthorpe, though, with Woolford dragging wide from six yards after Rob Jones' knockdown four minutes before the whistle.
Newcastle remained unsettled at the back after the restart, especially under the high ball, and Hooper crashed a rising effort against the angle of post and bar after Danny Simpson and Zurab Khizanishvili were outjumped by Paul Hayes.
But, to the delight of a record Glanford Park crowd of 8,921, Scunthorpe did open the scoring 53 minutes in, with Woolford finally finding his range.
Khizanishvili was the culprit from Newcastle's point of view, as, when facing his own goal, he allowed himself to be shrugged off the ball by Hooper, who unselfishly squared for the former York winger.
Geremi could have brought his side level moments later when he lashed over, but Nolan showed him how to do it with 25 minutes to go as he grabbed his seventh goal of the season.
It was a picture book goal for Nolan, as he arrived right on time on the edge of the area to hammer home into the bottom corner after a storming break from Danny Guthrie had created the chance.
Nolan again went close with a diving header after Ryan Taylor's cross, but rather than sit back and defend a point, Scunthorpe pressed for a winner which duly arrived 11 minutes from the end when Woolford got on the end of Sam Togwell's header to waltz through Newcastle's absent defence before leaving Harper with no chance.