"Now we've crossed that line we want to stay the right side of it," said Rovers manager Alan Lewer.
"With the players we had missing I must regard it as a point won rather than two points lost."
Rovers lost Jon Richardson before the kick-off when he pulled a thigh muscle in the warm-up, but the visitors still enjoyed the better of the early play.
As the game progressed Fleet's Jean Michel Sigere got behind the visitors' defence frequently, but it was Rovers who enjoyed the best effort of the first half when Hugh McAuley's 31st minute volley struck the Fleet woodwork from 30 yards.
With five men across the midfield Rovers shackled the Fleet and grew in confidence as the game unfolded.
McAuley was head and shoulders above anybody else on show, and he set up lone striker Charlie Griffin for a drive on 60 minutes which forced home keeper Paul Wilkerson into a low save.
It was a pedestrian performance from the Fleet and well-organised Rovers could have secured all three points with nine minutes remaining.
A McAuley free-kick was headed back by Griffin, requiring Sigere to head clear from under his own crossbar.