City needed Fielding to keep out a fizzing effort from David Ball as the game threatened to get away from the League One leaders.
Two minutes into the second half, City took the lead for the first time as Aaron Wilbraham played in Agard and the forward bagged his third goal since joining the Robins.
By the 51st minute, Steve Cotterill's men had put daylight between the sides as Agard turned provider for Wilbraham, who calmly slotted into the bottom right corner of Maxwell's net.
Fleetwood pulled a goal back when Morris played in Jamie Proctor and the second-half substitute headed the ball beyond the reach of Fielding.
City looked likely to score again and almost did when Korey Smith saw his 77th-minute effort saved by Maxwell.
However, they were pegged back in the 89th minute when Stephen Dobbie rifled home to give Town a point, but Peterborough United's loss at Yeovil means that the Robins now have a five-point lead over second-placed MK Dons.