Jake Beesley was hand with his second brace of the week, while Jordan Rhodes claimed his 10th goal of the season.
Kyle Joseph was also on the scoresheet, as he came off the bench for his home debut.
The result sees the Seasiders move level on points with Barnsley and Derby County, who are in sixth and seventh respectively, but have played more games than the teams above them.
Dan Grimshaw was called into action two minutes into the match, as the Blackpool keeper got down well to push away a Tom Bayliss effort.
Down the other end, it was Blackpool who claimed the opening goal of the afternoon.
Rhodes produced a superb flick into the path of Karamoko Dembele, with the former Celtic wonderkid tripped in the box.
From the penalty spot, the Huddersfield Town loanee stepped up and made no mistake, sending Marko Marosi the wrong way to claim his 10th goal of the season.
The Seasiders doubled their lead just after the half hour mark.
CJ Hamilton found space down the right side, and played the ball to Beesley at the front post.
The striker’s initial effort hit the keeper, but deflected into the net off him on the rebound, as he continued his scoring run after claiming a brace in the EFL Trophy win over Morecambe on Tuesday night.
Following the restart, Marosi made a great double save to stop Blackpool from extending their lead further.
He initially got a hand on a shot from distance from Sonny Carey, before denying Beesley from close-range.
With just over 20 minutes remaining, Bloomfield Road was finally introduced to summer signing Joseph, who came off the bench for his home debut.
Shortly after his introduction, he made his mark, smashing the ball past the Shrews keeper to make it 3-0.
Things got even better for the Seasiders, as Beesley claimed his second of the game.
The striker did well to control a great pass through by Joseph, before taking the ball around Marosi to finish.
Here’s how the Seasiders performed:
1. How did Blackpool perform?
We've taken a look at the performances of the Seasiders. Photo: CameraSport - Dave Howarth
2. Dan Grimshaw- 7
There wasn't too much for Dan Grimshaw to do between the sticks. The Seasiders made an early save to deny Tom Bayliss, but other opportunities were scarce. Photo: CameraSport - Lee Parker
3. Matthew Pennington- 7
Matthew Pennington enjoyed a solid enough afternoon against his former side. During the first half, the defender almost had a goal, with a header from a corner blocked in front of goal. Photo: CameraSport - Lee Parker
4. Marvin Ekpiteta- 7
Marvin Ekpiteta remained in Blackpool's starting 11 despite Olly Casey's availability after suspension. He certainly made a good claim for the position with a solid display. Photo: CameraSport - Dave Howarth
5. James Husband- 8
In Ollie Norburn's absense, James Husband received the captain's armband once again. He led the team well, and was a key part of the Seasiders' defensive control during the game. Photo: CameraSport - Lee Parker
6. CJ Hamilton- 8
It was a good afternoon for CJ Hamilton, who looked like a threat down the right side on a number of occasions. The wing-back played a key role in Beesley's first of the afternoon. Photo: CameraSport - Lee Parker