Owen Beck wasted the best chance of the early exchanges as the Rovers full-back found himself free at the far post from Andreas Weimann's nod down, but he blasted over the bar from six yards.
Storey had taken a knock from a heavy challenge earlier in the half and his evening came to an end after 30 minutes with Whatmough coming on.
Three minutes after Ryan Ledson had fired wide for Preston, some patient build-up from the home side ended with Gueye beating Whatmough to a Tyrhys Dolan cross and heading past Freddie Woodman.
It could have been worse for Preston just before the break, but Ryan Hedges sent his effort wide from Callum Brittain's pull-back.
Dominic Hyam headed wide for the home side shortly after the interval, before McCann wasted a golden chance to equalise as he headed over from close range.
Whatmough almost made up for his earlier mistake with an assist on 71 minutes, but Greenwood failed to make the most of his knock down.
Blackburn were handed the chance to double their lead three minutes later as a backpedalling Whatmough caught Hyam's chin with his head and referee Josh Smith pointed to the spot.
Cantwell stepped up confidently to send Woodman the wrong way for his second league goal of the season.
A late flurry from Preston threatened to derail Blackburn's second win in 10 matches, firstly as Emil Riis had a goal disallowed for offside when Whatmough's header appeared to be going in before the striker touched the ball over the line.
Then, three minutes into the six of added time, Potts controlled on his chest at the far post and beat Pears.
The visitors were left fuming in the dying seconds when Gueye appeared to catch Potts with an arm to the face, but referee Smith waved away their penalty appeals before blowing the final whistle moments later.
The result moves Blackburn up to fifth and ends the four-game unbeaten run of Preston, who remain in fifteenth.
Blackburn boss John Eustace told BBC Radio Lancashire:
"I thought we were excellent and should have been out of sight in the first half.
"We played some fantastic football and I was really pleased to go in at half-time 1-0 up, and the way the lads battled and stuck together in the second half I thought we deserved the victory.
"We've conceded a sloppy goal at the end which is disappointing, but it's a local derby so I'm really pleased we could get three points and do the fans proud."
Preston head coach Paul Heckingbottom spoke to BBC Radio Lancashire:
"We were too easy to play against in the first half in terms of not causing them enough problems, playing in front of them too much, and our attacking players weren't positive enough.
"We put ourselves in a horrible position being 2-0 down - we'll always focus on what we do, what we can do better, what we get right and wrong, but it's frustrating how the game ended."
On the award of a penalty against his side and not being given one late on:
"I've never seen a penalty given for a clash of heads but I have seen them all the time for elbows in faces - simple.
"We've not decided the game, that's the big issue, and when it's really frustrating."
Image source, Getty Images
