New Coventry signing Taiwo Awoniyi scored inside five minutes in a midweek Carabao Cup win over Plymouth Argyle, and he was lively early on here as well, forcing Nobel Mendy into a smart block after a darting run in behind.
The Nigerian then nodded a header just wide of the post, although the offside flag went up anyway.
His next effort was on target, with no intervention from the assistant referee this time, and he should really have asked more of Hull goalkeeper Konstantinos Tzolakis.
There was still time for yet another Awoniyi chance before the break, and the striker forced a better save from Tzolakis, but the two sides went in level at half-time.
The Tigers certainly hadn’t threatened a signature mauling in the first period, and Sergej Jakirovic made two changes at the break, introducing Lucas Gourna-Douath and Cody Drameh.
The visitors did look a little more imposing as a result, and Mendy tested Carl Rushworth for the first time with a stinging effort from outside the box.
The Sky Blues turned to their bench as well, and Brandon Thomas-Asante looked lively, although the corner he won came to nothing after Bobby Thomas was penalised for clearing out Tzolakis.
Tigers substitute Liam Millar then had a golden chance, dragging his effort narrowly wide after he had ghosted in behind the hosts’ back line.
The Canada international wasn’t going to turn down a second opportunity of such quality, though, and he slotted home a cool finish after a quickfire break from a Coventry corner to snatch the win dramatically.
The defeat means Coventry are still yet to open their Premier League account for the season, and it also ends Frank Lampard’s personal unbeaten record against Hull as a player and manager (W9, D5, L1).
Against the odds, Hull maintain their perfect record and can enjoy a temporary berth in second place in the table.
Flashscore Man of the Match: Konstantinos Tzolakis (Hull)