The Premier League strugglers found themselves in deep trouble midway through the first half when more basic errors allowed the visitors to take a strong grip on the contest thanks to Mark Beevers and former Derby striker Marcus Tudgay.
But Wednesday's defending was equally inept and Kenny Miller and Giles Barnes hit back to allow Derby to go in level at half-time.
Both teams had chances to win the game in the second half, but the final result was about right and Derby will be relieved to have avoided what would have been a morale-sapping defeat.
For Wednesday, the fact that they allowed a two-goal advantage to slip away will be disappointing, but they more than matched their opponents on an afternoon when there was plenty of goalmouth incidents to entertain a 20,000 plus crowd.
More than 5,000 of those made the short journey down the M1 and they were soon cheering the first goal of the match, when Beevers drove a left-foot shot into the net off the body of goalkeeper Lewis Price.
It was a bad goal for the Derby keeper to concede, but his team should have been level in the 16th minute when Gary Teale headed the ball across goal and Craig Fagan lifted his shot high into the visiting fans from only four yards out.
That miss looked to be even more vital because in the 23rd minute a dreadful mistake by Darren Moore allowed Tudgay to get in on Derby's left and drive a right-foot shot across Price from 12 yards.
If Tudgay had done better with a header from six yards in the 36th minute, it would probably have been the end of Derby, but instead Miller pulled one back in two minutes when Fagan's looping header dropped to the Scottish international, who beat Lee Grant from 12 yards.
It was poor defending and there was more uncertainty to come in the 44th minute when a corner was only cleared as far as Barnes who volleyed the equaliser with his left foot from 15 yards.
It seemed unlikely that the scoring would stop there and it needed a smart save by Price to deny Tudgay in the 50th minute and another excellent stop by Grant to keep out a Teale shot in the 74th minute.
Both teams pressed hard for a winning goal, but the result was about right and now the Rams have a replay which is the last thing they will have wanted.