Chris Burke looked to have set the visitors on their way to a comeback with a stunning strike in the 70th minute.
Shrewsbury had raced into the lead with goals from Jon Taylor and Tom Bradshaw in the 8th and 11th minute respectively.
Matt Green pegged Blues back seconds after the break before Burke struck in style. However two quick sucker punches from Paul Parry and Darren Jones condemned Blues to defeat.
Graham Turner's men came storming out of the blocks early on and Taylor stunned Blues' backline. After a dash down the left channel, he cut inside and fired a low shot beyond Colin Doyle despite the best efforts of Dan Burn on the line.
It was quickly 2-0 to the hosts. A neat one-two down the right saw John Bearsford tee up Bradshaw to stab home from close range. As Blues began to settle and recover from Shrewsbury's whirlwind start, Lee Clark's side started to string together goal-scoring opportunities.
But it was after the break when those chances came to fruition. Green set the tone for stunning strikes in the 46th minute by thumping home a 20-yard effort, with the help of a deflection, beyond Joe Anyon.
Then it was the turn of some trademark Chris Burke. The Scotland international was quick to pounce on Green's blocked shot, switched the ball on to his left foot and bent an effort from the edge of the area into the left corner.
Burke almost set up substitute Shane Ferguson for a winner in the 75th minute after a dazzling run down the right only to see the Northern Irishman's shot blocked out by a defender.
However, Shrewsbury swiftly caught Blues on the break when Parry exquisitely lobbed the stranded Doyle from 25 yards. It was game over two minutes later when Shrews substitute Jones was given too much space on the edge of the area to drive home a low shot.
Shrewsbury Town starting XI: Anyon; Bearsford, Jacobson, Summerfield, Winfield, Mkandawire, Wildig, Marsden, Bradshaw, Parry, Taylor. Subs: McQuaid, Weale, Woods, Jones, Goldson, McAllister.
Blues: Doyle; Little, Robinson, Burn, Davis (Hancox 63); Allan (Reilly 79), Adeyemi (Higgins 79), Shinnie (Ferguson 63); Burke, Green (McGurk 79), Elliott. Subs: Randolph, Eardley, Bartley, Lee, Arthur.
Attendance: 2,037 (707)