A half-time power cut, which lasted for 35 minutes and blacked out large parts of the city, threatened to derail managerless Caley's celebrations.
However, the affected sub-station was eventually restored to full capacity giving Billy McKay, who scored twice, and Aaron Doran time to add to Nick Ross's 45th minute penalty.
McKay ended any hope of a fightback from the Championship side with goals in the 71st and 88th minutes before Doran completed the scoring from the spot in injury time after Ton's Scott Taggart was shown a red card.
Inverness, who had U20 coaches Duncan Shearer and Scott Kellacher in temporary charge following the departure of Terry Butcher, went into the game on the back of four successive victories and quickly gained the upper against their lower-league opponents.
McKay missed a golden chance to score early on when he shot wide after fine work from Doran and the latter went even closer minutes later when he saw his 18-yard strike fly just inches wide of the visiting goal.
And they were almost made to pay when former Rangers striker Nacho Novo latched onto a misplaced pass from Ross Draper but his dipping 25-yard volley was tipped over by keeper Dean Brill.
This sparked Caley into life and Draper tried his luck from 20 yards before visiting keeper Nicolas Caraux pulled off a superb save to keep out a stinging volley from McKay.
Caraux was again called on to deny McKay before Caley's pressure finally told when Craig Reid was adjudged to have fouled Draper in the box allowing Ross to convert from the spot with just seconds of the opening period remaining.
After the enforced delay, the game assumed a similar pattern as the first half with Doran and McKay both going close as Caley looked to kill off the visitors.
Draper then struck the woodwork and Ross fired over from 10 yards before McKay finally grabbed the killer goal 19 minutes from time.
The in-form striker got on the end of a Marley Watkins cross to send a looping effort beyond the helpless Caraux at the back post.
Two minutes from time he scored his 13th of the season when tapping home from close range before Doran completed the scoring from the penalty spot after Taggart saw red for upending substitute Torbjorn Agdestein as he raced in on goal.