The Shrews hit the front just three minutes in at the Racecourse Ground, as home defender Dennis Lawrence turned Neil Sorvel's free-kick past his own keeper, Michael Ingham.
Things got much, much worse for the Red Dragons 15 minutes in as Ingham beat away a Glynn Hurst header, but as the ball headed goalwards Dean Bennett handled on the line.
He was immediately dismissed by referee Mr Beeby and Colin McMenamin tucked away the resulting spot-kick to double Town's lead.
There were no more goals before the break, but Shrews boss Gary Peters did withdraw Steven Hogg after he was booked for a reckless tackle on Darren Ferguson.
Wrexham introduced Lee McEvilly at the interval to try and find a foothold back into the game and the striker hit the outside of an upright with a free-kick as Denis Smith's side pushed forward.
At the other end sub Mark Stallard almost extended Town's lead as the game opened up.
Twelve minutes from time Wrexham were back in the game as loan striker Matt Derbyshire turned the ball home from close range after a corner by Ferguson was flicked on by Danny Williams.
It looked like the Blackburn youngster had used his hand, but the goal stood and took his tally to nine in ten games for the Red Dragons.
When McMenamin was red-carded for a rash tackle on Jonathan Walters the home side sensed a point was there for the taking, but Mark Jones and Derbyshire were denied in a frantic finale.