Two weeks on from a thrilling late 3-2 victory away to Celtic, the inconsistency that has dogged Rangers' season looked set to strike again as they twice trailed by two goals at Dens Park.
Simon Murray and Joe Shaughnessy put Dundee 2-0 up inside 20 minutes.
Shaughnessy's own goal brought the visitors back into the game late in the first half before Scott Tiffoney blasted home to make it 3-1.
Rangers rallied thanks to two fine strikes from outside the box from captain James Tavernier and Tom Lawrence.
Dessers had missed a series of chances throughout the game but finally got on the scoresheet with his 10th attempt on goal after Aaron Donnelly failed to deal with Tavernier's long ball.
Another memorable win may prove fruitless in Rangers' pursuit of Celtic at the top of the table, but does Barry Ferguson's case to make his interim spell in charge a permanent one no harm.