Ryan Hedges opened the scoring in the first half with a delightful finish, before goals from Yuki Ohashi and new captain Todd Cantwell rounded off a strong performance.
Rovers’ starting eleven remained unchanged from last weekend’s late defeat to Birmingham City, with the only change on the bench as Felix Goddard made his first matchday squad, replacing Nick Michalski in the substitutes.
It was the visitors that started the opening 15 minutes the strongest, with the front four of Kargbo, Cantwell, Hedges and Ohashi linking up well, but no chances came to fruition, with the final ball typically lacking.
This allowed Hull to grow into the game, with Oliver McBurnie’s header from close range being well saved by Toth, before Joel Ndala cut inside and curled goalwards but the Rovers shot-stopper was equal to it.
The close calls gave a much-needed wake-up call to Rovers, and they responded as they took the lead on 18 minutes. Augustus Kargbo played a well-weighted pass to Ryan Hedges, who expertly dinked the ball over the onrushing Pandur to give the away side the lead.
From there on, chances were few and far up to the break, with Kargbo coming the closest as he drove forward, but his shot was dragged wide.
The half ended in typical fashion, with pinball in the box saw the ball fall to McBurnie, but his effort was tame and Rovers held on into the break.
Rovers started the second half strongly and doubled their lead within two minutes. Cantwell stood over the free-kick looking to cross the ball, but cleverly played a quick pass to the unmarked Hedges, who squared for Ohashi to make it two.
Just two minutes later, newly-announced permanent captain Cantwell made it three. The marauding Alebiosu got into the box and squared the ball, and Cantwell was there to pick up the loose ball and fire home past the stranded Pandur.
The two quick-fire goals took the sting out of the match, with Rovers coming close to adding a fourth soon after as Dom Hyam clattered the crossbar with a header, before Sidnei Tavares volleyed over from close range.
Hull tried to make their way back into the match, but solid defending and a lack of cutting edge from the hosts saw their efforts wasted, with substitute David Akintola squandering the best chance after miscontrolling a simple pass at the back post.
Rovers could have added insult to injury with several attacks towards the end, but some last-ditch defending kept the scoreline down.
The victory gives Rovers a needed three points, with focus now turning to Norwich’s visit to Ewood Park next Saturday.
Toth; Alebiosu, Hyam, McLoughlin, Ribeiro; Tronstad, Tavares (Montgomery 70’); Kargbo (Henriksson 70’), Cantwell, Hedges (De Neve 86’); Ohashi (Gueye 86’). Unused: Goddard, Wharton, Pickering, Miller, Tyjon.
Referee: Tom Nield
Attendance: 20,518