The former York winger raced clear of a pedestrian Rams defence and beat Stephen Bywater to get the Iron up and running on their return to the second tier.
Gary Hooper had put Nigel Adkins' side in front twice in the first half either side of goals from Paul Green and Kris Commons.
The home side had spurned several first-half opportunities and although Derby looked more threatening after the break they were caught cold by Woolford late on in what was the first competitive game between the two clubs since 1964.
After an uninspiring opening 15 minutes the game suddenly burst into life with two goals in the space of three minutes.
It was the home side who struck first, when Woolford found space inside the area and Bywater could only parry his left-foot strike into the path of Hooper, who fired home from point-blank range.
The goal seemed to spark Derby into life and they drew level minutes later with a composed finish from Green.
The former Doncaster midfielder ghosted forward and took a perfectly-weighted pass from Stephen Pearson in his stride before beating Joe Murphy with a measured right-foot finish.
Hooper missed a golden opportunity to restore Scunthorpe's lead after 25 minutes when he went one-on-one with Bywater, but failed to hit the target.
And Hooper's strike partner Paul Hayes was also wasteful in front of goal six minutes later, firing wide from the angle.
Scunthorpe's front two continued to cause problems in Derby's defence and Hooper spurned yet another excellent opportunity when he beat the offside but failed to find a way past Bywater.
And Green should have made them pay just before half-time when he fired wastefully wide.
That miss proved costly when the Rams' defence was caught out a minute later, with Hayes playing in Hooper and he fired home a right-foot finish off the post.
But Derby drew level on the hour-mark when Murphy brought down the onrushing Green in the penalty area and Commons made no mistake with the resulting spot-kick.
Commons was in the thick of the action soon after when Murphy rushed off his line and the Scotland forward crossed towards the empty net, but the ball was scrambled away by a retreating Scunthorpe defender.
The Rams looked increasingly dangerous on the break and Lee Croft crossed for Commons, who failed to get enough power on his header.
But Derby were caught out with nine minutes remaining when Woolford was played through in the right channel and kept his composure to slot the ball past Bywater.