The Glasgow giants defeated Viktoria Plzen 3-0 in the first leg of a Champions League qualifier on Tuesday. They had previously overcome Panathinaikos to get closer to a return to Europe's top competition.
However, this marks the first time since 1989 that they have failed to win either of their first two league matches.
Dundee manager Steven Pressley had a difficult start to his tenure, suffering two defeats to lower league teams that led to their elimination from the League Cup at the group stage. They were convincingly beaten at home by Hibernian on the opening weekend of the new league season.
Yet, they were left to regret not achieving a memorable victory at Ibrox after Ryan Astley's looping header gave them the lead early in the second half.
Rangers were reduced to 10 men when Nasser Djiga received a straight red card for denying a clear goal-scoring opportunity.
The home side did manage to rally in stoppage time to at least earn a point when Djeidi Gassama was fouled, and captain James Tavernier, who had been benched for the second consecutive game by Martin, converted the penalty.
Cyriel Dessers believed he had clinched all three points, only to have his goal ruled out for offside.
Celtic have the opportunity to extend their lead to four points over their city rivals when they travel to Aberdeen on Sunday.
Earlier, Livingston defeated Falkirk 3-1 in the clash of the newly-promoted teams.
Motherwell and St. Mirren failed to capitalize on their strong performances against the Old Firm on the opening weekend, ending in a 0-0 draw.
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