Morten Gamst Pedersen set Sam Allardyce's side on their way with his first goal of the season just past the half-hour mark and Benni McCarthy wrapped up the points from the penalty spot with his 10th league goal of the campaign.
Portsmouth, who remain in the relegation mix-up on 38 points, had a late opportunity for a consolation goal but substitute John Utaka skied his spot-kick three minutes from time.
Before the game, Rovers made one change to the side that lost away at Manchester City last time out, with Keith Andrews coming in for the injured Andre Ooijer at right-back.
Portsmouth made two changes to the side that lost 3-0 at home to Arsenal, with Younes Kaboul and Glen Johnson shaking off thigh injuries to replace Noe Pamarot and Jermaine Pennant.
As the game kicked off, the heavens opened at Ewood Park, with both sides struggling to find their feet on the slippery surface early on.
Long balls to targetmen Chris Samba and Peter Crouch were subsequently deemed the best course of action.
After a disappointing opening display, the game sprung to life around the half-hour mark courtesy of some neat interplay from the home side.
McCarthy's back-heel sent Stephen Warnock scampering down the left wing and his cross was almost turned in by a Portsmouth player.
But just two minutes later and Rovers were celebrating the opening goal. Warnock's cross-field pass was controlled by Samba on his chest and as the makeshift striker lunged to shoot, David James failed to gather and Pedersen was on hand to slot home.
Portsmouth's best chance of the half arrived just two minutes before the break, but Hermann Hreidarsson's downward header from Sean Davis' free-kick bounced just wide of the right-hand post.
Almost immediately after the restart, Richard Hughes shot straight at Paul Robinson, but it was the home side who looked more likely to add to their tally.
On 47 minutes, Pedersen's long throw was flicked on by Samba to Warnock, but his goal-bound shot deflected inches wide off Kaboul.
Five minutes later, El-Hadji Diouf's corner was headed home by Samba, but the DR Congo international was penalised for a foul on Sol Campbell.
But on 58 minutes, Rovers did double their lead. McCarthy's ball into the box struck the arm of Hreidarsson and the South Africa striker coolly stepped up to slot home from the spot.
Portsmouth manager Paul Hart went for broke, making three changes in quick succession and the trio were immediately involved in an attacking sense.
On 70 minutes, Crouch played the ball out wide to substitute Pennant, whose cross-shot just eluded the far post.
Four minutes later and the other two combined, as Kanu slipped in Utaka, who rounded Robinson, but then saw Ryan Nelsen get back to block on the line.
The same Portsmouth duo were involved in the final chance of the game as Kanu's cross struck the arm of Andrews inside the box, but Utaka failed to follow McCarthy's example after blazing high and wide from 12 yards.