Shrewsbury got off to a flying start when Ian Woan's right-wing corner curled directly into the net, although Andy Dibble got a touch to it.
Luke Rodgers went close to doubling the lead when his first-time rising shot from the edge of the area cleared the crossbar.
Wrexham recovered from the early setback and began to increase the pressure on their ex-keeper Mark Cartwright in the Shrews goal.
He nearly made a mistake when he dropped a cross from Darren Ferguson but gathered the ball at the second attempt before Andy Morrell could get a touch.
Ferguson set up Wrexham's first real chance only for Jim Whitley to curl a hurried shot wide. Wrexham levelled on the half-hour when Lee Trundle collected a Ferguson free kick and chipped in from close range.
Shrewsbury were ahead again within three minutes when Brian Carey missed Nigel Jemson's cross and Jamie Tolley beat Dibble with a header at the near post.
Carlos Edwards had a shot blocked on the Shrewsbury line, before Darren Moss made a goal-line clearance from Carey before Morrell headed Wrexham level from another Ferguson free kick.
Back came the Shrews to take the lead again, Alex Smith crossing for Jemson to add the final touch.
It was good value for Wrexham's biggest league crowd of the season and the home side were soon back on terms again, Trundle setting up Paul Edwards to add their third goal.
Shrewsbury boss Kevin Ratcliffe said: "There was a lot of pride and passion out there on both sides. It was nice for the fans but not nice for managers." A disappointed Wrexham manager Denis Smith agreed it was a great game to watch but added: "We should have had three points. We made enough chances to have won.
"That early goal gave Shrewsbury time to take their throw-ins and goal kicks while we wanted to get on with the game."