The game was marked by controversy. Rangers were denied two good claims for a penalty and Aberdeen took the lead after 57 minutes with a penalty which appeared altogether more generous.
However, Rangers had contributed to their own downfall because Richard Gough and Ally Maxwell failed to clear the ball. Duncan Shearer was brought down by the goalkeeper to concede the penalty, from which Billy Dodds scored.
With three minutes remaining, Shearer took advantage of a mistake by Stuart McCall to score a second goal for Aberdeen and give them their sixth win of the season. The victory improved their position in the League from second bottom to fourth bottom.
Aitken, who replaced Willie Miller last week, was delighted by his team's performance. He said: "I said if my players gave me their best we'd win - and they did. It was a great effort by my players and everyone here was committed to Aberdeen, including the crowd, who showed their respect for Willie Miller."
Aitken said arguments about two penalty claims for Rangers would be "nit- picking", and Walter Smith, the Rangers manager, also refused to be drawn on the decisions.
Rangers, though, remain 14 points clear of the field. With 11 games remaining there are very few people who would bet against them collecting a seventh successive championship.
Rangers' success this season can be partly traced to their rivals failure to win enough games to sustain a challenge. Celtic drew again, the 15th time in 25 matches, against Hibs at Hampden.
Tommy Burns, the Celtic manager, is in search of new players, and he must look to bring in ones who will not settle for a share of the points. Celtic, not for the first time this season, were twice ahead and were twice clawed back.
With money available to buy players, Burns has been searching the continent. However, Celtic's chief executive, Fergus McCann, could face a court battle to keep some of the money. Superstadia, the company charged with designing the ill-fated Cambuslang stadium for the previous board, have indicated their intention to sue for £250,000 plus VAT for work completed.
The only other game in the Premier Division to escape the weather took place at Tynecastle, where Hearts and Kilmarnock fought out a 2-2 draw.
In the First Division, St Mirren supporters resisted calls for a mass walk-out at the start of the second half, despite the fact that their side were trailing Raith Rovers 2-0.
The organisers had hoped that 1,000 supporters would follow them as a protest against the manager, Jimmy Bone, whose side have only won three games all season. However, only a handful of people joined the protest.Reuse content