Paul Trollope's men put out Fulham in their third round replay on Tuesday and, after a nervous start which saw goalkeeper Steve Phillips save Jason Puncheon's second-minute penalty, they grew in confidence with Rickie Lambert's header earning a deserved victory.
But the League One side started slowly and were lucky not to fall behind to Paul Fairclough's men, who sit 26 places below them in the Football League pyramid.
It took only two minutes for them to crumble as Ashley Carew's driven cross struck the arm of centre-half Joe Jacobsen, leaving referee Steve Bennett with little option but to point to the spot.
Puncheon has been tipped for bigger things than the lower end of the league, but his effort lacked conviction as Phillips went low to his left to pull off a comfortable save.
The game continued at a frenetic pace as Rovers, heading down the infamous Underhill slope in the first-half, responded, Chris Lines forcing Lee Harrison to tip his volleyed strike over from close range.
But just four minutes into the second period the visitors took the lead. The goal owed much to David Pipe, who escaped three challenges on the right before swinging in a cross that begged to be converted.
Lambert duly obliged for his fifth FA Cup goal of the season and 12th in all.
Trollope's side resolved to play on the break from then on as the game settled into a familiar pattern of a Barnet attack breaking down, with a counter-attack from their technically accomplished opponents promising more of a threat.
And that tactic was sufficient to see the game out with ease, and they will hope to draw a big fish and a potentially lucrative windfall in the last 16, while Barnet will now concentrate their efforts on securing their league status.