Jake Beesley was also on the scoresheet with a brace while Jordan Rhodes moved his season tally into double figures, as Neil Critchley’s returned to winning ways in League One.
The result marks the Seasiders’ first victory over the Shrews since 1997, with 10 defeats and three draws coming in-between.
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.
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.
Blackpool FC: Dan Grimshaw, Matthew Pennington, Marvin Ekpiteta, James Husband, CJ Hamilton (86’), Kenny Dougall, Sonny Carey (67’), Owen Dale (81’), Karamoko Dembele (81’), Jordan Rhodes (67’), Jake Beesley.
Substitutions: Richard O’Donnell, Callum Connolly (81’), Albie Morgan (67’), Kyle Joseph (67’), Jensen Weir (86’), Olly Casey, Andy Lyons (81’).