After being outplayed for the bulk of the first half in which they fell behind to a Declan Gallagher header, the Gers were much better after the interval and deservedly drew level with a superb free-kick from Arnold Peralta.
It was a much changed Rangers team from that which faced Albion Rovers on Ramsdens Cup duty at the weekend. With the exception of Luca Gasparotto at the back and Kyle McAusland in midfield, who would most likely give way to Lee McCulloch and Ian Black respectively, Ally McCoist had gone for arguably his strongest side to face his old team-mate John Brown's outfit. But it was the Dens men who made the brighter start.
Riley and Conroy were off target with early efforts, with Rangers only response coming from a neat link up between summer signings Jon Daly and Nicky Clark but the former Queen Of The South striker's shot was comfortably gathered by goalkeeper Letheren.
Rangers were slack at the back and Dundee were perhaps guilty of making one pass too many when a more direct approach might have been more rewarding. Monti and MacDonald missed good chances and it looked like just a matter of time before the home side went ahead.
Yet it was Rangers who came closest to breaking the deadlock after 39 minutes. David Templeton struck the wall with a free-kick, the ball looped into the air, Nicky Clark was first to react and got in a header, only to see it clip the post.
Three minutes before half-time Dundee made the breakthrough and, not for the first time, defending a corner kick proved to be Rangers' undoing. Riley flighted the ball into the near post area and Gallagher rose unchallenged to glance his header past the helpless Cammy Bell.
Clearly Ally McCoist had words with his team during the half-time break and they were much more impressive after the interval.
Nicky Law fired a low shot wide of goal as the Gers pushed forward and they got the goal their more menacing approach merited in the 61st minute. A mazy Templeton run ended with the winger being scythed down on the edge of the box and Arnold Peralta beautifully curled his free-kick into the postage stamp corner of the net.
At this point Rangers looked the likelier winners. McAusland shot over the top, then his replacement Robbie Crawford didn't make clean contact with the ball after battling to create the shooting opportunity and his effort was saved.
Dundee regained the upper hand in the latter stages but Rangers held out quite comfortably.
DUNDEE (4-4-2): Letheren; McAlister, Gallagher, Davidson, Lockwood; Riley, McBride, Rae, Conroy; MacDonald, Monti. Subs: Dyer, Doris, Benedictus, Reid (for Lockwood, Riley, Conroy, Monti 64 mins), Boyle, Wighton (for MacDonald, McAlister 74 mins).
RANGERS (4-4-2): Bell; Foster, Mohsni, Gasparotto, Smith; Peralta, McAusland, Law, Templeton; Daly, Clark. Subs: Crawford (for McAusland 64 mins), Aird (for Templeton 74 mins).
Referee: Greg Aitken.
Attendance: 5,244