Uche Ikpeazu's two goals confirmed his status as Hearts' new hero and helped his club reach the Betfred Cup knockout phase.
Ben Garuccio lashed home a free-kick in between Ikpeazu's brace, and Steven Naismith's second-half double sent Inverness Caledonian Thistle out of the competition on goal difference.
Hearts progress having finished top of Group C despite a two-point deduction for fielding the ineligible Andy Irving in their opening game against Cove Rangers. Anything other than victory would have eliminated them from the tournament, but they produced a second successive 5-0 win to go through.
Ikpeazu joined from the English League Two club Cambridge United just a few weeks ago and is already a favourite amongst the Tynecastle support. The striker scored in Tuesday's 5-0 triumph against Cowdenbeath and followed up with an impressive double allied to Garuccio's exquisite free-kick and Naismith's two headers.
Ikpeazu took Kyle Lafferty's place in Hearts' starting line-up as the Northern Irishman had a back complaint. He was also the subject of a ￡200,000 transfer bid from Rangers on Friday. There was a first start for Aaron Hughes on the right of a four-man home defence.
Inverness arrived with two former Tynecastle players in their side – goalkeeper Mark Ridgers and defender Brad McKay. Manager John Robertson, though, had the strongest maroon connection as Hearts' record league goalscorer. He was warmly cheered and applauded onto the pitch by the home support before kick-off.
The noise continued once play began. The hosts fired several early crosses into the visitors' penalty area begging for a conversion. Coll Donaldson, the Inverness defender, cleared two just in time, and Ridgers also punched a couple to safety.
Hearts looked comfortable in a 4-4-2 formation having previously used a three-man defence this summer. Inverness set up 4-3-3, with wingers retreating whenever their team was out of possession. It suited a counter-attack, which almost produced the game's opening goal on 14 minutes.
The Highlanders sprung forward and Tom Walsh fed midfielder Joe Chalmers to his left for a first-time attempt which rolled just past goalkeeper Zdenek Zlamal's far post. Hearts responded from a set-piece, John Souttar's free-kick clipped into the penalty box by Steven Naismith for striker partner Ikpeazu to head goalwards. Ridgers was sharply across to his right to hold the bouncing ball.
Olly Lee had delivered several dangerous Hearts corners approaching the half-hour mark, and it was another of those which produced the game's first goal. The English midfielder dispatched an outswinger towards the penalty spot and Ikpeazu fought off a marker to volley the ball into Ridgers' net.
That sparked a Hearts goal frenzy. Three minutes later, after Donaldson impeded Naismith, they doubled their advantage. Garuccio stepped up to send a dipping 22-yard free-kick over the wall and into the top corner with Ridgers beaten. Ikpeazu claimed his second, and Hearts' third, 90 seconds later with a pinpoint header from Garuccio's left-sided cross.
Effectively, the game was now over before half-time. Inverness deserved credit for refusing to quit but they faced a mountainous task. Zlamal made two important saves to deny Walsh and then used his fingertips to prevent Charlie Trafford's header reducing the deficit. Inverness were mindful that a four-goal defeat would eliminate them.
Lee struck the post with a 25-yard attempt before the break and Hearts continued their controlled, passing performance after the interval. Zlamal required another fine save to thwart Chalmers before Naismith headed Callumn Morrison's cross home for the fourth goal.
Lafferty climbed off the bench to hit the post before Naismith claimed his own second goal. The Scotland forward rose to meet Lee's cross and guide a looping header away from Ridgers and in at the far post. That finished off an excellent afternoon's work and sent Hearts confidently into the Betfred Cup's last 16. Partick Thistle go through on goal difference ahead of Inverness.
Hearts (4-4-2): Zlamal; Hughes, Souttar, Berra, Garuccio (McDonald 83); Morrison, Haring, Lee, Naismith; Ikpeazu (Burns 79), MacLean (Lafferty 66). Unused subs: Doyle, Bozanic, Mulraney, L Smith.
Inverness CT (4-3-3): Ridgers; Rooney, McKay, Donaldson, Tremarco (Calder 58); Polworth, Trafford, Chalmers; Walsh (Mackay 72), White, Doran (Austin 61). Unused subs: Hoban, McCart, Oakley, Elbouzedi.
Referee: Willie Collum.