Derek McInnes's men had been on a seven-game winning streak, including two victories over Celtic last month, to close in on their Glasgow rivals after a slow start to the campaign.
But Dundee were well worthy of a point in a performance that showed why they sit fourth in the table.
Ashley Hay rattled the Rangers crossbar with a towering header before Bradley Fink coolly rounded Ivor Pandur to put the home side in front.
Badredine Bouanani's stunning strike into the top corner quickly brought Rangers level before half-time.
Nico Raskin then produced an ever better hit from long range to give the visitors the lead.
However, Dundee were gifted an equaliser 20 minutes from time when Dan Neil was dispossessed deep inside his own half by Callum Jones, who slotted into the bottom corner to secure a point.
Celtic host third-placed Hearts on Sunday in the first clash between the sides since the Hoops snatched the title from the Edinburgh side in the final moments of last season.
Victory would open up a four-point lead at the top of the table for Martin O'Neill's side, while Hearts could close to within one point of the leaders with a win.
Hibernian slipped to the bottom of the table after Marink Reedijk's home debut as manager ended in a 2-1 defeat to Falkirk thanks to Jacob Murrell's double.
Greg Kiltie scored twice to lift Kilmarnock above Hibs with a 3-2 win over struggling Motherwell.
Aberdeen beat St. Mirren 3-1, while St. Johnstone and Dundee United played out a 1-1 draw.