Bristol City's Tony Butler came closest to breaking the deadlock in a dull draw at the Racecourse when his header crashed against the crossbar.
Wrexham, though, had the better chances in an evenly-matched first half.
Hector Sam was lively but wasteful and spurned a great chance to open the scoring when he
failed to connect with a Carlos Edwards cross early on.
The Trinidadian should also have scored on 19 minutes but he chipped over the bar
with just the keeper to beat.
Sam then narrowly failed to reach Chris Llewellyn's goalbound header on 39
minutes before Darren Ferguson slashed a drive wide of the upright.
City started the second half in more positive mood, but the Dragons had the
best early chance on 55 minutes when Edwards forced Steve Phillips into a smart
Lee Jones fired wide when put through on 63 minutes and his strike partner Sam
followed suit six minutes later.
Butler then hit the woodwork from a Luke Wilkshire corner on 75 minutes, but
as the match wore on neither side could force a winner.
Wrexham: Dibble, Roberts, Carey, Lawrence, Carlos Edwards,
Whitley, Ferguson, Llewellyn, Paul Edwards, Lee Jones, Sam.
Subs: Holmes, Whitfield, Morgan, Mark Jones, Thomas.
Bristol City: Phillips, Carey, Butler, Coles, Bell, Wilkshire,
Doherty, Tinnion, Aaron Brown, Miller, Peacock. Subs: Hill,
Burnell, Stowell, Roberts, Woodman.
Referee: M Clattenburg (Co Durham)