As their contrasting positions would suggest, Hull started the brighter of the two, with Liam Millar and Regan Slater testing the home defence, but the first half gradually drifted into a cagey, stop-start affair.
Blackburn’s best spell of the game in terms of possession came after half-time, their best chance falling to newly acquired striker Mathias Jorgensen, who headed over just before the hour mark.
Tigers boss Sergej Jakirovic rang the changes after the break but but it was Koumas and Joseph – both brought on the 76th mark – who would be the decisive substitutes.
Only five minutes after his introduction, Scotland Under-21 international Joseph was fed through by Hadziahmetovic and squared it to Liverpool loanee Koumas to score from close range.
Koumas then nearly returned the favour in the 89th minute with a ball into the box but Joseph was denied by a smart save from Rovers’ Balasz Toth.
The defeat leaves Rovers still mired in the Championship relegation zone ahead of Tuesday’s home game against Sheffield Wednesday, while Hull extend their strong run to keep up the pressure on the top two.