Rickie Lambert's goal early in the second half was enough to send Bristol Rovers into the fifth round of the FA Cup for the first time in nine years.
Lambert's goal was enough to send the Pirates through
Rovers goalkeeper Steve Phillips saved Jason Puncheon's second-minute penalty after Danny Coles was controversially adjudged to have handled in the area.
Barnet were made to rue that miss when Lambert headed home David Pipe's cross.
Goalkeeper Lee Harrison twice denied Lambert his second goal of the match in the closing 10 minutes.
The home side did have chances, and Phillips kept out two Cliff Akurang efforts in quick succession.
Barnet enjoyed a spell of pressure after the break and Neal Bishop's attempt from the edge of the area flew just past the mark.
Puncheon, desperate to make amends for squandering his side's early chance, sent in a thunderous 25-yard drive but Coles was able to get his body in the way to avert the danger.
Barnet became restricted to speculative efforts and Ashley Carew saw his long-range shot blocked by Chris Lines as Rovers began to sit back and protect their lead.
It was Rovers who looked the more likely to grab the game's second goal and Sammy Igoe nearly did just that 15 minutes from time, when he dragged a shot wide of the target.
Barnet: Harrison, Devera, Bishop, Yakubu, Nicolau (Birchall 69), Puncheon, Porter, Carew (Thomas 69), Gillet, Wright, Akurang (Grazioli 82).
Subs Not Used: Hendon, O'Cearuill.
Bristol Rovers: Phillips, Lescott, Hinton, Coles, Jacobson, Pipe (Igoe 65), Campbell, Disley, Lines, Lambert (Walker 85), Williams (Rigg 80).
Subs Not Used: Carruthers, Anthony.
Goals: Lambert 49.
Ref: Steve Bennett (Kent).