Breaking away leaders Birmingham moved a step closer to securing automatic promotion in Sky Bet League One with a 4-1 victory in Michael Appleton's debut game as Shrewsbury's manager.
The match was dominated by Birmingham from the beginning to the end under the guidance of Blues head coach Chris Davies, who was overseeing his 50th game in charge.
The action saw Keshi Anderson narrowly miss with an angled half volley, and Jay Stansfield's shot was saved by goalkeeper Jamal Blackman in a one-on-one situation.
Willum Willumsson missed the target with a curled effort, while Kieran Dowell failed to find the net after an exchange with Anderson and a clever dummy by Willumsson.
Ben Davies opened the scoring for Blues in the 27th minute, finishing off Dowell's free-kick from close range without being marked.
Blues' dominance was evident as Marc Leonard's shot deflected behind off Aaron Pierre.
Laird extended the lead to 2-0 in the 61st minute, heading home Leonard's delivery without any challenge.
Alfie May scored from close range to make it 3-0 after 77 minutes, capitalizing on Emil Hansson's cross while being left unmarked.
May completed his brace in the 86th minute, rounding Blackman and finishing a pass from Louis Harris.
In a rare attacking opportunity for the visitors, substitute Vadaine Oliver headed in a consolation goal just a minute later.