A defensive clanger by Aberdeen defender Thomas Solberg gifted Rangers three vital points at Pittodrie.
The match had been poised at 11 at half-time before Solberg allowed Ronald de Boer to rob him. Michael Mols accepted an easy chance from de Boer's pass to notch the decisive goal.
Aberdeen had taken an early lead through Arild Stavrum but Kenny Miller equalised before the break to re-emphasise his reputation as the hottest striker in Scottish football.
The home side had gone 405 minutes without a goal before this match but needed little more than 240 seconds to end that drought as Rangers began a defensive performance that for the first half was as bad as it gets.
In the end, Ebbe Skovdahl's team went in at the break having scored just that one goal, Stavrum's stabbed finish from Kevin McNaughton's cross from the right.
The recalled Norseman nipped in ahead of Lorenzo Amoruso and Scott Wilson with such ease that it was clear Rangers' defensive problems were far from over.
The malaise also spread upfield with the normally touch-perfect Mols letting the ball run out of play through his feet.
Then he sent a pass meant for de Boer out of play as the champions looked in complete disarray.
But Miller had other ideas and fired his side's first shot in anger in the 24th minute, forcing Ryan Esson into a good save.
Esson had to repeat the trick when an Amoruso shot from a freekick move was deflected towards the bottom corner and Rangers duly equalised with a goal of true, and on such a night entirely unexpected, quality.
Mols turned Derek Whyte to set up Miller for a rasping left-foot shot into the bottom corner and that took the youngster's amazing scoring record to nine in five starts. He even has another goal on his tally, one from coming off the bench against Kilmarnock.
The second half was a different story once Solberg had gifted Rangers the lead, allowing himself to be dispossessed by de Boer collecting a short goal kick.
De Boer's ball to Mols bypassed Esson and despite a man on the line Mols had no trouble finding the net.
Derek Young, who had earlier been booked for an over-zealous challenge, repeated the offence on Wilson and was sent off to leave his team-mates to play the final 20 minutes a man down.
It summed up the way the balance of the game had tilted away from the home side. And crucially, despite the odd nervy moment, Rangers no longer looked vulnerable at the back.
ABERDEEN: Esson, Rowson, Solberg, Whyte, McNaughton (McAllister 77), D Young, D Young, Guntveit (Mayer 80), Clark (Di Rocco 59), Winters, Stavrum. Subs Not Used: Preece, Perry. Sent Off: D Young (69). Booked: D Young, Whyte. Goal: Stavrum 5.
RANGERS: Christensen, Ricksen, Amoruso, Konterman, Wilson (Adamczuk 80), Vidmar, de Boer, Ferguson, Albertz, Mols, Miller (Dodds 72). Subs Not Used: Brown, Ross. Booked: Amoruso, Konterman, Ferguson. Goals: Miller 40, Mols 50.
Referee: M McCurry (Scotland).