Two goals from Darren Mackie in the first half sent Aberdeen into the last eight of the Scottish Cup.
Mackie (right) notched a double
The home side took the lead after 15 minutes when Mackie got in between Ross Tokely and Grant Munro to head home Kevin McNaughton's deep cross.
Craig Brewster levelled the scores nine minutes later, when he stabbed home Richie Hart's free-kick into the box.
Mackie slammed home his second after 34 minutes, when Mark Brown could only parry a Jamie Winter free-kick.
Inverness started well and laid siege to the Dons goal throughout the opening 10 minutes.
Richie Hart's delivery from the right was causing Aberdeen problems and they conceded three corners in quick succession.
Aberdeen had offered little in the opening stages but were ahead on 15 minutes with a fine goal from Darren Mackie. The striker got in between Ross Tokely and Grant Munro to meet McNaughton's deep cross.
Mark Brown committed himself to coming for the ball but was badly out of position and the ball looped over him.
Aberdeen could not hold on to their advantage, however, as Brewster brought his team back on level terms in the 24th minute.
He again found space in front of Michael Hart and toe-poked Richie Hart's cross from the right beyond Ryan Esson.
The woodwork was rattled again in the 25th minute, this time by Stuart Golabek, who blasted an audacious effort from 18 yards.
Aberdeen took the lead for the second time with Mackie's 10th goal of the season.
The 23-year-old followed in on the goalkeeper and reaped the reward after he palmed Jamie Winter's ferocious long-range shot into his path.
Aberdeen should have extended their lead after the interval but Whelan produced what will have to be considered one of the misses of the season.
The striker casually approached Mackie's low cross and, standing unmarked a few yards out, allowed the ball to bounce off his shin.
Mackie swept the ball into the area again, this time for Craig, but he bounced a header off the bar.
Whelan's miserable afternoon continued in the 77th minute.
Once again Mackie picked him out unmarked inside the box and again he pulled a shot well wide.
Dons manager Jimmy Calderwood mercifully brought his afternoon to an end immediately afterwards with Derek Adams coming on.
Caley tried to chase the game towards the end, but the Dons rearguard held firm and edged closer to Hampden.
Aberdeen: Esson, Hart, Anderson, Byrne, McNaughton, Mackie (McGuire 88), Heikkinen, Winter, Clark, Craig (Stewart 69), Whelan (Adams 80). Subs Not Used: Blanchard, Morrison.
Goals: Mackie 15, 34.
Inverness CT: Brown, Tokely, Dods, Munro, Golabek, Wilson, Duncan, Juanjo (Fatai 77), Hart (McBain 70), Bayne, Brewster. Subs Not Used: McCaffrey, Prunty, Jonathon Smith.
Goals: Brewster 24.
Ref: W Young