Despite plenty of territorial advantage it took until the 79th minute before the Dons got the vital breakthrough.
Not for the first time this season the cultured left foot of Charlie Mulgrew created the opening for Gary McDonald to gleefully head past Ryan Esson and give the home side a vital three points in their charge for a place in next season's Europa Cup.
The visitors opened brightly and forced a couple of half-chances. From the second of them, Filipe Morais stepped away from the group before trying to pass the ball into the net from 18 yards. However, Jamie Langfield in the home goal got down smartly to save at his left-hand post.
Aberdeen almost got the opener after 17 minutes. Derek Young and Chris Maquire combined and, from the latter's excellent cross, the ball found the head of Lee Miller, but the effort was brilliantly parried away by Esson.
The visitors had another let-off minutes later. Jamie Smith's corner found Lee Mair rising unchallenged at the far post but the big centre-back couldn't direct his downward header on target.
Midway through the half Sone Aluko's cross evaded the Caley defence and the ball fell to Young who took a touch before blasting the ball off Grant Munro and away from the danger area.
In the 27th minute Aluko played the ball to the far post where Miller was only inches away from getting a vital touch.
With the game approaching half-time Aberdeen created one final chance. A Richard Foster long throw was only partially cleared to the edge of the area. The ball fell into the path of McDonald, but the tall midfielder's left-footed effort drifted wide of the upright.
Inverness were fortunate in the 55th minute when Aluko's cross was fumbled by Esson. The ball was scrambled away to the edge of the area where McDonald's first-time shot deflected off Ian Black, allowing Munro to hack the ball off the line.
In the 57th minute the visitors had an amazing let-off. Aluko skipped past Ross Tokely and smashed in a left-foot drive which was only parried by Esson, into the path of Chris Maguire.
His effort ricocheted off the face of the crossbar with Miller only able to knock the rebound over the crossbar.
Aberdeen's territorial advantage finally paid off in the 79th minute when a deep cross from Mulgrew found McDonald climbing high above his marker to lob a header over Esson and into the net.
The home side went looking for a second goal and it nearly arrived with four minutes left.
Scott Severin played the ball into the path of Mair who swept in a great shot from the edge of the box. Esson dived to turn the ball away and Mair only just failed to net the rebound.