The Potters ended a run of four successive league defeats in comprehensive fashion as Rovers' troubles continued.
Stoke's victory increased the pressure on Rovers manager Steve Kean, who has now won just six times in 34 league matches, as Ruben Rochina's late consolation had little impact.
Rovers remain mired in the bottom three and this performance highlighted why, despite Kean's insistence that they have not played badly this season.
Blackburn have just one victory this season and have taken only three points from their last eight games.
With form like that, it is surprising that owners Venky's sanctioned a new contract, confirmed this week, for the Rovers boss.
Stoke may have lost their last two home games but the other pre-match statistics gave little encouragement to Blackburn and those figures only worsened on a blustery afternoon in the Potteries.
Rovers have now lost the last four meetings, although they finally ended a goal drought against the Potters which had lasted 599 minutes.
Understandably, considering both teams were low on form and confidence, there was little for the crowd to get excited about in the first half, which could be summed up in three incidents.
Two of those involved Blackburn midfielder Steven Nzonzi and his flailing elbows which caught Ryan Shawcross and then Whelan in the head in separate incidents about three minutes apart.
The ball spent much of the time in the air, which was not a good ploy in the wind swirling around the stadium but did help in the creation of the opening goal.
Stoke's first genuine chance to threaten the Rovers goal came when Nzonzi's foul on Crouch presented Jermaine Pennant with a free-kick from the right.
He produced a perfect delivery and Delap got in front of Gael Givet to divert a glancing header past goalkeeper Paul Robinson and inside the far post.
By contrast, Blackburn's first free-kick in a dangerous area was drilled straight into the wall by Pedersen and even when they did get a shot on target from Scott Dann's header Whelan comfortably cleared off the line under no pressure.
Blackburn should have equalised within a minute of the second half after Rochina had dribbled his way to the byline and cleverly backheeled to Mauro Formica but the Argentinian completely missed his shot from four yards.
There followed a brief interruption in play due to a number of black bin bags blowing across the pitch which could easily have represented some bizarre, ironic review of the game so far.
When the action resumed, Robert Huth was left wondering how he missed the target as he powered a header wide from Matt Etherington's far post cross in the 54th minute.
But fortunately for Stoke they did not have long to rue that error as four minutes later Etherington picked out Jon Walters in the penalty area and he laid the ball off for Whelan, with the aid of a deflection from Dann, to drive home from 25 yards for his first goal since February 2010.
The match was wrapped up in the 72nd minute when Crouch clinically converted Marc Wilson's long ball into the Rovers penalty area with a left-footed shot.
Walters then fired wide from the other side of the penalty area as Stoke threatened to run amok.
When Rovers finally threatened, it was too little too late as Rochina fired home from distance in the 86th minute after Hoilett had cut in from the left and Nzonzi had delivered the final pass for the Spaniard.
The final whistle brought relief for Stoke but more grief for Kean and his Blackburn team.