Mark Yates' side bossed the opening 45 minutes and took a deserved lead after 24 minutes, midfield maestro Marlon Pack with a 20-yard effort which squeezed past Fleetwood stopper Scott Davies.
They could have doubled their advantage before the break, Davies tipping Sam Deering's blast over the crossbar.
The Robins looked in total control - right up to the moment Fleetwood equalised, Junior Brown with a bullet header from a Ryan Crowther corner.
Davies produced two fine saves to keep the scores level, first denying Pack a second, turning his low drive around the post, then pulling of an incredible reflex save to thwart Paul Benson from point blank range.
Jon Parkin had a late penalty shout turned down when the ball looked to strike a hand in the Robins box as Fleetwood ended the game on the offensive.