Caley Thistle fielded new signing Gil Blumenshtein, while on-loan Hibernian full-back Kevin McCann also started in a team which also included young winger Nick Ross, who had done well for the club during pre-season.
David Murray for Craig Smith was the only change for a Queen's Park team that already had one competitive match under their belt this season when overcoming Livingston 3-2 in the first round of the Alba Challenge Cup last Saturday.
It took Inverness 18 minutes to register their first shot on target against a team three leagues below them - Adam Rooney firing in a low shot from 18 yards which was comfortably held by visiting goalkeeper Peter Hamilton.
Caley Thistle were controlling proceedings and four minutes later they took the lead.
Good work from Ross allowed him time on the edge of the box to slip the ball through to Lee Cox, who despite having his initial effort saved by Hamilton, reacted quickly to slide the rebound into the unguarded net.
Ross was proving a real handful on the right and he set up Kevin McCann moments later to deliver a cross that Blumenshtein should have converted, but he could only head wide from six yards.
The hosts might have dominated the opening half, yet they almost went in at the interval on level terms.
Ricky Little found himself with some room on the right and his low cross was only inches away from being converted by the unmarked Ian Watt at the near post.
Inverness were forced into making a change at half-time as Grant Munro succumbed to a knock and was replaced by another summer arrival, Chris Innes at the heart of the home defence.
Eric Odhiambo then came on for Blumenshtein in the 54th minute and his arrival had an immediate impact as Caley Thistle doubled their lead a minute later.
Rooney's flick-on should have been dealt with comfortably by goalkeeper Hamilton, but he dallied over his clearance allowing Odhiambo to close him down with the ball striking the forward and rebounding into the back of the net.
Queen's Park had barely had time to clear their heads at the loss of such a poor goal before they found themselves further behind in the 57th minute.
A corner from Danni Sanchez was not properly cleared and as the ball fell to defender Ross Tokely, who showed great composure to smash home from 10 yards.
The visitors were now all but out of the competition, but they did have a chance to reduce the deficit when substitute Paul Harkins strode through the centre of Caley Thistle's defence only to see Ryan Esson produce a smart save low to his right.
Caley Thistle then had to conduct another reshuffle as Innes lasted only 14 minutes before an injury ended his afternoon. Roy McBain came on with Stuart Golabek reverting from left-back to centre-half.
There had been few nervy moments for Inverness to endure, but they survived a late scare when the lively Watt flashed a shot across the face of goal.
In the final few minutes, Odhiambo almost scored his second of the game only for Hamilton to get enough on his save to keep it out, despite Paul Burns almost putting the attempted clearance into his own goal.