League One: Fleetwood 0 Barnsley 0
Graham Alexander's men have now failed to score in three consecutive matches, while the result moved Danny Wilson's team two points clear of the relegation zone.
It took just minutes for Fleetwood to create a fine opportunity at Highbury Stadium, but Gareth Evans failed to get enough height on his attempted dink on Wednesday.
Stephen Dobbie and Jamie Proctor also threatened for Fleetwood, who breathed a sigh of relief when Dale Jennings' strike rattled the woodwork.
Fleetwood threw everything forward in the second half, but some resolute defending and the reflexes of goalkeeper Adam Davies kept the deadlock intact.
In the final minute of normal time, Fleetwood's Josh Morris unleashed a fierce strike which was denied by the crossbar.
Fleetwood will try to win for the first time in seven games in all competitions when they face Bristol City on Saturday, while Barnsley travel to second-bottom Port Vale.