The weather didn't help as light rain and a swirling wind caused problems for both sides.
After an opening 20 minutes that was easily forgettable the game came to life in the 25th minute when Shrewsbury forward Grant Holt brought a fingertip save from Darlington keeper Simon Brown.
The home side responded with a shot from Franz Burgmeier that was dealt with by Town keeper Luke Daniels.
The game was notable for a string of strange refereeing decisions that reached a zenith in the 39th minute when Darlington defender Neil Austin brought a save from Daniels with a low shot from outside the area that was tipped around the post.
The visitors were awarded a goal kick and nobody in the stadium was surprised at the decision. Holt brought another save out of Brown two minutes later, the keeper saving the strikers effort at the second attempt to keep the score level.
Ten minutes into the second period the home side took the lead following a foul by Holt on Burgmeier that brought a yellow card for the Shrews forward and a one-match suspension.
Burgmeier took the kick and defender Alan White sent a powerful header beyond Daniels for his second goal of the season.
Darlington striker Liam Hatch almost increased his side's advantage with a header that had Daniels scrambling across his goal-line in the 64th minute.
The visitors grabbed an unlikely equaliser seven minutes later through midfielder Sean Thornton. There seemed no danger for the home defence until Thornton unleashed an unstoppable shot from 30 yards that flew over Brown to earn his side a valuable point on their travels.