The Bees gifted the home side a two-goal lead in the game and then came storming back, twice going within inches of grabbing a draw.
Shots from both Giuliano Grazioli and Liam Hatch crashed against the crossbar in the final minutes as Rovers desperately held on to end a run of three defeats.
It was always open, devil-take-the-hindmost football as both teams sacrificed defensive cover to put everything into attack.
The action had still been drawing its first breath when Richard Walker put Rovers ahead. Barnet had just charged down a Junior Agogo shot but were off balance as James Hunt hurried the ball back into their goal area.
Defenders were caught out and Ross Flitney was off his line as Walker swept his shot into an empty net.
To score first is a rare luxury for Rovers, but Barnet were close to equalising within minutes when Nicky Bailey, running their midfield, sent a long low shot just wide of Scott Shearer's right post.
Ismail Yakubu, who had failed to close down Walker for the first goal, was again caught out when the striker grabbed his second and 12th of the season.
A static midfield had been opened up by Hunt and Stuart Campbell and Walker, bursting in from the left, scored with a clean strike.
Rovers had no time to sit back on their lead and were tested when Ian Hendon, from just over the half way line, hit his trademark crosses towards the far post.
Twice corners were scrambled away and there was a lucky escape for the home side when Shearer lost his footing trying to reach his far post. A long punt from Simon King went just wide of target.
Shearer, though, got down well to field a sharp drive from Dean Sinclair. Barnet were now well in the game and began to boss the second half.
Their spirits soared when Ben Strevens rose with a determined header out of their fifth corner to make it 2-1 as the game moved into its final third.
Their fight back came at some cost as they collected four bookings to one for Rovers for Campbell, who stupidly kicked the ball away at a free-kick.