Bradley Fink gave the home side the lead at Dens Park, before Rangers responded with goals from Badredine Bouanani and Nico Raskin.
However Callum Jones got the equaliser for Dundee midway through the second-half which saw the points shared.
There was one change from last weekend’s victory over Kilmarnock as Badredine Bouanani came in to replace Kevin Kelsy.
Dujon Sterling made his 100th competitive appearance for the club starting in defence alongside Emmanuel Fernandez, Olwethu Makhanya and James Penrice, with Ivor Pandur in goal.
Dan Neil captained the team in midfield, with Nico Raskin and Minsu, while Djeidi Gassama and Badredine Bouanani provided the support for Ryan Naderi.
Dundee had a positive start to the season themselves, and Alan Forrest tested Ivor Pandur inside the opening 15 minutes. He picked up the ball in midfield and drove forward before releasing a right-footed strike towards goal but it was gathered comfortably by the Rangers number one.
Gers were struggling to create any clear cut openings as the home side pushed for a breakthrough with a couple of chances around the half-hour mark.
The first came from a free-kick, as Ethan Hamilton whipped the ball into the box, with Ryan Astley’s looping header tipped over the bar by Pandur.
From the resulting corner, again delivered by Hamilton, Ashley Hay rattled the post with a header.
At the other end, Dujon Sterling delivered from the right with it breaking for Dan Neil in the box, but his strike was just wide of the target.
Ethan Hamilton had a chance of his own as Dundee looked to capitalise as they regained possession inside the Rangers half but he flashed his shot wide of the target.
The pressure from the home side paid off as they took the lead with 38 minutes played. A long ball forward from Hamilton had Astley and Dujon Sterling battling for the ball. Sterling got a touch but it broke for Bradley Fink who finished low beyond Pandur.
The goal sparked a reaction from Rangers and they responded just five minutes later with an equaliser. Badredine Bouanani’s initial strike was blocked by a host of bodies in the box, but it fell again for the winger, and this time he made no mistake in curling a left-footed shot beyond Owen Goodman for his first goal for the club.
Into the second-half, McInnes’ men seemed to have taken a lift from that first-half equaliser as Minsu came close with a shot flashed wide, before Bounanani forced Goodman to push wide an effort minutes later.
Gassama was next to come close for Gers as Nico Raskin fed a pass to the winger. He turned well before sending a powerful right-footed hit towards goal which looked to be heading for the bottom corner, but Goodman was alert to push wide.
Fink saw a header saved by Pandur as he got on the end of a free-kick swung into the box by Callum Jones.
Rangers had the lead as the game approached the hour mark and it was a special goal from Nico Raskin. The ball broke for the Belgian midfielder and he sent a superb right-footed strike from over 25-yards out towards goal which beat the goalkeeper and went in off the bar.
Goodman saved a Gassama effort with his feet before Bouanani was denied by the keeper as Rangers pushed for a third.
However despite the pressure, Rangers gifted Dundee an equaliser as Callum Jones nicked the ball off Dan Neil on the edge of the box and sent a low strike beyond Pandur to level the game once again.
Neil almost had Rangers back in the lead as it fell for him in the box but it was cleared off the line by Owen Bevan.
There was a double change with 15 minutes remaining as Kevin Kelsy and Findlay Curtis came on to freshen Rangers’ attack in place of Minsu and Badredine Bouanani.
James Penrice saw a shot go high of the target as Rangers searched for a late goal to get the three points.
In added time, Gassama had a low shot deflected wide as Gers were unable to find a late winner.
RANGERS: Pandur, Sterling, Fernandez, Makhanya, Penrice, Neil, Raskin, Minsu (Kelsy, 75), Gassama, Bouanani (Curtis, 75), Naderi.
Subs: Kelly, Nedeljkovic, Godfrey, Rommens, Dragojevic, Chukwuani, Miovski.
Dundee: Goodman, Astley, O. Bevan, Wright, Hay, Samuels, Forrest, Fink, J. Bevan (Harrison, 66), Jones, Hamilton.
Subs: O’Hara, Halliday, Odutayo, Akinmboni, Finnigan, Besir, Reilly, Wright