The Daggers took the lead after just five minutes when Shaun Beeley was adjudged to have handled inside the penalty area after the visitors had twice hit the crossbar.
Medy Elito converted the resulting spot-kick to hand the visitors a lead which would last just one minute.
Junior Brown may have intended his ball from the right channel as a cross, instead it crept in at the back post to bring play-off outsiders Fleetwood level.
And before the break they could have been ahead, first Jamille Matt tested goalkeeper Chris Lewington before referee Andy Haines blew for a Fleetwood free-kick just as Jamie McGuire was tapping the ball home.
Town were in charge and they took a deserved lead early in the second half, winger Evans cutting in from the left and firing home an unstoppable 20-yard shot.
Substitute Jake Reed forced a save from Fleetwood's Scott Davies as the Daggers looked to battle back but the hosts held on to claim the spoils.