David Ball's double saw Shrewsbury drop back to the foot of the League One table as Fleetwood swept them aside at Highbury.
Shrewsbury frustrated the hosts in the opening stages, but Uwe Rosler's side finally found a way through in the 38th minute to continue their record of scoring in every league game.
Amari'i Bell fed Devante Cole on the left and he fizzed the ball across the six-yard box for Northern Ireland full-back Conor McLaughlin to fire home.
Bell was again influential as the hosts doubled their lead, pulling back for Ball to net his seventh of the season in the 53rd minute, after Shrewsbury had failed to fully clear
Ball was in the action 20 minutes later as the forward sublimely wrapped his right foot around the ball and curled it into the top corner from just outside the area.
The striker carved out a number of late opportunities but just missed out on completing his hat-trick as Fleetwood moved up to eighth and within a point of a play-off spot, while Chesterfield's win at MK Dons condemned Shrewsbury's return to bottom spot after consecutive losses.
Report supplied by Press Association.
