Remarkably, it is the first time in 17 seasons that Aberdeen have recorded two league wins in a campaign over Rangers.
The Light Blues have not looked the most solid at the back in recent matches and their defensive frailties were exposed twice before half-time.
Dutchman Ferne Snoyl, on loan from Feyenoord, was the architect of the opening goal in 33 minutes as he drifted past Bob Malcolm and then whipped in a cross which Jamie Smith, seemingly unmarked, volleyed into the net from 10 yards.
The irony was that the strike came at a period in the game when Rangers looked reasonably threatening.
A minute before the Aberdeen goal the returning Dado Prso won a corner following some excellent endeavour.
Peter Lovenkrands whipped over the dead ball and Marvin Andrews was presented with a glorious near post chance but headed the ball over the top.
Sixty seconds later he was counting the cost when he failed to pick up Smith, who finished with some style.
If that was not bad enough, Rangers were totally exposed again two minutes before half-time.
Ian Murray was beaten in the air by Smith, who flicked the ball on perfectly for Steve Lovell who had the simplest of chances to drill the ball past Ronald Waterreus who was utterly helpless.
Alex McLeish was furious and he made two changes at half-time to try to change the course of events, although one was enforced.
Thomas Buffel came on for Kris Boyd and was sent to play on the left side with Lovenkrands moving into a more advanced position.
Soto Kyrgiakos had to come off with a thigh muscle injury and Stevie Smith came on to play left back with Murray moving to centre back.
In fairness, there was more purpose about Rangers in the early moments of the second half and skipper Barry Ferguson had a decent chance four minutes in.
Smith and Burke worked a good move on the left side with the latter teeing up Ferguson but he slid his left foot shot wide from 12 yards.
Five minutes later the captain was in the box again looking to get on the end of a Lovenkrands cross. He threw himself at the ball but his header went wide.
This was encouraging for McLeish and he must have thought Rangers were back in the game in 59 minutes when Prso sent Buffel scampering into the right side of the Dons’ box.
The Belgian looked up and cleverly squared the ball for Lovenkrands. Inexplicably, the Dane shot wide with his right boot from eight yards.
A minute later Prso tried a long range shot which Langfield fumbled but Burke could not take advantage as his cross was cleared by Russell Anderson.
Rangers had all of the play but they could not make their pressure and the frustration only increased.
There were some other near things but at the end of it all Rangers looked a team lacking in ideas and that has to be addressed with so many crucial games coming up.
ABERDEEN: 20-Langfield; 11-Clark, 4-Anderson, 6-Severin, 3-McNaughton; 8-Nicholson, 31-Griffin, 29-MacFarlane (5-Diamond 76) 15-Snoyl (19-Foster 66); 9-Lovell (10-Mackie 73), 7-Smith.
Subs not used: 1-Esson, 14-Dempsey, 16-Stewart, 22-Macaulay.
Bookings: Foster (89)
RANGERS: 25-Waterreus; 2-Ricksen, 5-Andrews, 14-Kyrgiakos (34-Smith, 45), 24-Murray; 17-Burke, 6-Ferguson, 12-Malcolm, 26-Lovenkrands; 15-Boyd (4-Buffel 45), 9-Prso.
Subs not used: 1-Klos, 42-Carcary, 20-Hutton,10-Novo, 7-Hemdani.
Bookings: Prso (87)
Ref: John Underhill.
Man of the match: Chris Burke