The Glasgow giants thrashed Viktoria Plzen 3-0 in the first leg of a Champions League qualifier on Tuesday. They had already seen off Panathinaikos to close in on a return to European football's elite competition.
However, they have failed to win either of their first two league games for the first time since 1989.
Dundee boss Steven Pressley had endured a torrid start to his reign as two defeats to lower league opposition saw them eliminated from the League Cup at the group stages. They were soundly beaten at home by Hibernian on the opening weekend of the new league season.
Yet, they were left to rue not securing a famous victory at Ibrox after Ryan Astley's looping header opened the scoring early in the second half.
Rangers were then reduced to 10 men when Nasser Djiga was shown a straight red card for denying a clear goalscoring opportunity.
The home side did rally in stoppage time to at least secure a point when Djeidi Gassama was brought down and captain James Tavernier, who had been dropped from the start for the second consecutive game by Martin, converted the penalty.
Cyriel Dessers thought he had secured all three points only to be denied for offside.
Celtic have the chance to move four points clear of their city rivals when they travel to Aberdeen on Sunday.
Earlier, Livingston beat Falkirk 3-1 in the battle of the newly-promoted sides.
Motherwell and St. Mirren failed to build on their positive displays against the Old Firm on the opening weekend in a 0-0 draw.