In a rescheduled contest that had been postponed in November due to a waterlogged pitch, it was the away side who went closest in the first half when Colby Bishop struck the crossbar shortly before half-time.
But substitute Makhtar Gueye headed Rovers in front just past the hour mark and Callum Brittain cracked in a second in the 71st minute, moments after Bishop's header was cleared off the line.
Andreas Weimann added the third soon afterwards as Blackburn recorded a first triumph in six league outings and moved up two places to fifth spot.
John Mousinho's Portsmouth are second bottom of the table after their fourth loss in five league games.