Chris Dagnall put the Iron ahead after just four minutes, clipping the ball in off a posit after collecting a through ball from Woolford.
Paul Hayes almost got a quick equaliser after a long ball found Josh King who laid the ball off for the former Iron man whose shot was parried away by Joe Murphy.
King did have the ball past Murphy after 13 minutes, but it was clearly offside.
Half-time brought one enforced change for the Iron, with Michael Raynes coming on in place of Rob Jones - who was struggling due to his broken hand.
Preston came out looking to get an early equaliser, with Darel Russell shooting straight at Murphy.
Freddie Sears, making his debut after joining on loan from West Ham earlier in the day, shot at the home keeper Andy Lonergan for the Iron's first chance of the second-half. Eddie Nolan fired the rebound wide.
Craig Morgan drew the home side level when he headed home a corner, taking advantage of slack defending from United.
Dagnall had an effort ruled out for offside before Preston took the lead after 63 minutes, again aided by poor defending from a corner. This time Billy Jones volleyed home.
Iron fans could have been forgiven for thinking heads would drop, but the match was tied again a minute later when Michael O'Connor curled home a free-kick from just outside the area.
Murphy's game was ended early due to a groin problem. He had indicated it was a problem at half-time but tried to play on.
Preston tried to test the rookie keeper, but the closest they went to scoring was a Paul Parry shot which went over the bar.
They were made to pay when a poor backpass went straight to Sears. His shot came back off a post, but Woolford was on hand to fire home the rebound from a tough angle and secure the win.