Before the match Tigers coach Grant McCann pleaded with his side: “don’t let it be like a rollercoaster where we have one win and then one defeat.”
Jarrod Bowen's neat 61st-minute finish gave his side back-to-back wins as the Owls suffered a third straight defeat in a laboured and subdued New Year's Day derby.
Sheffield Wednesday brought two well-paid former Premier League strikers off the bench in search of a goal in Steven Fletcher and Jordan Rhodes, but it is Hull who have the master finisher, and Bowen is surely a future Premier League player. Hull will just be hoping that future is at least half a season off yet.
Football is far too professional now for Championship players to be running around hungover, but it did feel like the end of a busy Festive period in the flatness of the game and the subdued Hillsborough atmosphere.
The Tigers were first out of their slumbers, Eric Lichaj having a shot blocked from the left. Hull's captain moved to the other side of the back four to fill the gap injuries have opened there.
The Owls' left-hand side offered the most excitement, with winger Kadeem Harris the best performer once the hosts found their feet. His ninth-minute run to the byline and cross presented Barry Bannan with a volley he was able to carefully measure up, but not put on target. Sam Winnall, preferred to Jordan Rhodes, alongside Steven Fletcher on the bench, also put a Harris centre wide, on the half-volley.
In his first start since August, centre-back Matthew Pennington was asked to fill the hole Lichaj left and he made decisive contributions at both ends to keep the game scoreless.
He did not seem to know what to do when Kamil Grosicki's 13th-minute corner found him unmarked at the back post, flopping onto the ball and chesting it wide.
When Adthe Nuhiu bundled his way to the byline and pulled the ball back for Harris in the 35th minute, an alert Pennington denied Harris the goal he deserved with a vital clearance.
Generally, though, the football was untidy, Cameron Dawson dropping a routine cross but recovering it before any excitement could break out, and Adam Reach stumbling onto another Harris delivery and putting it wide.
Dominic Iorfa's slide tackle on Grosicki as Jarrod Bowen tried to play him in was a rare and welcome moment of quality. He produced a repeat in the second half.
Fletcher's half-time introduction after three matches out with illness instantly gave his side more bite, and he hit the post at a scrambled 50th-minute corner.
He was also wide with a free-kick, grazed a Jacob Murphy cross off target and he and Rhodes just failed to stretch to a ball whipped in low by the substitute winger.
By then, though, the Owls were looking for an equaliser, not a winner.
An excellent run and cross by the energetic George Honeyman, building on his weekend performance, got the neat finish it deserved from Bowen, a winger with 17 goals already this season. It is not hard to work out why he is in demand.
Grosicki shot over minutes later with Wednesday preparing their final substitute but this was not a two-goal game. It was barely one-goal quality.
Hull will not care, having secured back-to-back wins for the first time since November 2. The Owls just need a bit extra in January.
Sheffield Wednesday: Dawson; Iorfa, Borner, Lees, Fox; Reach (Murphy 64), Hutchinson, Bannan, Harris; Winnall, Nuhiu (Fletcher 46).
Unused substitutes: Lee, Rhodes, Pelupessy, Odubajo.
Hull City: Long; Pennington, Burke, De Wijs, Lichaj; Batty, Irvine; Bowen, Honeyman (Lopes 72), Grosicki; Eaves.
Unused substitutes: Tafazolli, McKenzie, Bowler, Ingram, Fleming, Lewis-Potter.
Referee: J Simpson (Lancashire).