The Gunners - who now trail leaders United by seven points with a match in hand - had plenty of possession, but were unable to really test Paul Robinson in the Rovers’ goal.
The visitors had lost five of the last eight matches, but grew in confidence and survived the sending-off of midfielder Steven Nzonzi to earn a useful point in their battle against relegation.
With United coming from behind to win at West Ham earlier this afternoon, Arsenal could not afford another off day, but that is exactly what happened.