Yakubu set Rovers on their way to a priceless win with a 20th-minute opener on Saturday and finished the job from the penalty spot eight minutes from time before departing to a hero’s reception.
But despite a win which lifted Rovers off the bottom of the Premier League table, Kean still felt the ire of some home fans who continued to chant for his dismissal.
Brendan Rodgers’ Swans had hauled themselves back into the game with goals from Leroy Lita and Luke Moore, and were pressing for an equaliser when Joe Allen was sent off and then Neil Taylor gave away the spot-kick in quick succession.
Rodgers’ men had started brightly after a minute’s applause for Gary Speed, with Scott Sinclair causing problems down the left and drilling an eighth minute shot just wide.
Swansea’s early invention sparked the first signs of restlessness with the inevitable chants for Kean’s dismissal starting after Sinclair saw another dangerous cross blocked by Chris Samba.
Rovers failed to threaten at all until the 12th minute when Mauro Formica won a free-kick on the edge of the box, but Morten Gamst Morten Gamst Pedersen’s set-piece flashed wide.
Swansea keeper Michael Vorm had to punch away a deep free-kick from his opposite number Paul Robinson, as Rovers belatedly began to make an impression in the visitors’ half.
And Yakubu grabbed his first in the 20th minute after superb work from Gael Givet, who cut in from the left flank and crossed for the Nigerian to blast home the opener.
But even that goal did not placate some sections of the home support, who booed when Kean celebrated with the goalscorer on the touchline.
It was clear Yakubu was up for the challenge, but after sending another chance squirming wide it was the visitors who grabbed an equaliser in the 35th minute.
Mark Gower sent in a looping cross from the right flank and Lita, in for the injured Danny Graham, rose to angle a fine header in off Robinson’s left-hand post.
Yakubu restored Blackburn’s lead in first-half injury time when he reacted with a point-blank header after substitute Simon Vukcevic volleyed across the box.
Sinclair was at the centre of almost all Swansea’s moves early in the second half, setting up Lita to blaze over the bar then unleashing a shot of his own into the side-netting.
Formica shot just wide for Rovers then Yakubu had the ball in the net for a third time after being fed by Vukcevic, but was rightly adjudged to be inches offside.
Remarkably Robinson, the penalty box hero at Wigan a fortnight ago, played a big part in Rovers’ third when his booming goal kick was tipped over the bar by opposite number Vorm.
From the resulting corner, Rovers grabbed their third, with Samba heading back Pedersen’s set-piece and Yakubu pouncing to finally complete his hat-trick from close range.
But Swansea were far from done and they reduced the deficit in the 66th minute when Moore fired home from inside the box after Robinson had parried an initial effort from Wayne Routledge.
With nerves clearly jangling among the Rovers rearguard, Sinclair was given space to blaze over the bar before Taylor’s foul on Vukcevic allowed Yakubu to complete his solo show.
And, with Allen having been shown a second yellow card seconds before the goal, Swansea’s hopes were over.