Derrick Williams' first goal in over two years ensured Rovers made it two wins from two with a second 1-0 victory in the space of four days.
The Irishman struck just after the hour, nodding home from close range to earn a gritty victory on the road and secure a second clean sheet for Rovers.
In truth, it was probably deserved for Mowbray's men, although they were indebted to Christian Walton, who produced an excellent stop to deny Jarrod Bowen from the spot early into the encounter.
The woodwork came to both teams' rescue in the first half before Williams popped up with the winner.
Danny Graham dropped to the bench, with Adam Armstrong coming in to replace the powerful forward, in the only change made by Mowbray for the clash.
Rovers began well, and after George Long was forced to tip over a Greg Cunningham cross, Bradley Johnson nodded the resulting corner just wide after the Hull stopper failed to deal with a Stewart Downing corner.
But soon after the home side were awarded a penalty when Johnson was adjudged to have brought down Jackson Irvine in the box when trying to clear the danger.
Star man Bowen stepped up to the mark, but Walton guessed right to dive full stretch to his left and beat the attacker's powerful effort away and keep the score 0-0 after 12 minutes.
Johnson was having an eventful opening to the game and he guided a Cunningham cross onto the crossbar just moments later as Rovers looked to get a foothold in the lively encounter.
David Batty fired over after a perfect pick out from Poland international Kamil Grosicki as the chances continued to arrive for both sides in an open first half.
Back up the other end and brave goalkeeping from Long denied Armstrong from going round the stopper, before Irivine diverted another fine Grosicki cross just pass Walton's post.
Grosicki was being a thorn in the Rovers side, and he crashed a strike against the crossbar before curling an effort just an inch or two beyond Walton's left-hand post.
A brilliant flowing move at the other end saw Bradley Dack feed Downing, whose attempt bounced off the base of the post and away from danger as half time approached.
The influential Johnson clipped the upright again just two minutes before the break, as he got the perfect purchase to curl another lovely Downing pass towards goal from 25 yards.
Amazingly, despite the raft of opportunities for both sides, the teams went in at the break without a goal, but the deadlock was almost broken by Gallagher just four minutes after the interval, but the big forward skewed a header back across goal rather than into he back of the net.
Johnson was a relieved man on the hour when his pocket was picked by Batty, whose snapshot flew just past the post as Walton's clean sheet remained intact.
But the same couldn't be said of Long, who couldn't stop Williams from nodding home his first goal in over two years.
The Republic of Ireland international was in the right place to glance home Downing's free kick and put the visitors a goal up just after the hour mark.
An unbelievable last ditch challenge from Lewis Travis stopped a rampaging Bowen from testing Walton from an acute angle as Grant McCann's side looked for an instant response.
Long showed safe hands to hold onto a powerful drive from Long, before the home stopper ended a solo run and dink from Cunningham a minute later as Rovers looked to kill the game off.
Time was running out for the hosts to grab an equaliser, and substitute Leo Da Silva Lopes lashed over at the back post before a goal-saving challenge from Williams ensured Rovers went home happy and with the three points and clean sheet in the bag.
Hull City: Long, McKenzie (Da Silva Lopes, 74), De Wijs, Burke, Kingsley, Stewart, Batty (Bowler, 67), Irvine (c), Grosicki, Bowen, Eaves (Magennis, 67).
Unused substitutes: Ingram, Tafazolli, Toral, Fleming.
Booked: Stewart, 38, Eaves, 53, Kingsley, 61, Bowler, 80.
Rovers: Walton, Bennett (c), Lenihan, Williams, Cunningham, Johnson, Travis, Downing, Dack (Rothwell, 73), Gallagher (Graham, 63), Armstrong (Buckley, 90).
Unused substitutes: Leutwiler, Nyambe, Bell, Evans.
Goal: Williams, 61.
Booked: Lenihan, 81.
Referee: Robert Jones.