New signing Mohamed Bettamer made his debut for The Bees as he was one of three changes from the side who lost to Maidstone last weekend.
The Bees opened the scoring on 16 minutes through Craig Robson before Chris Lines slotted home a penalty in the second half.
The first chance of the game fell to the hosts after Elliott Johnson won a corner with five minutes on the clock. Jack Taylor whipped it in from the left before Robson headed the ball narrowly wide of the post.
Rovers were reduced to 10 men moments later after Sinclair received his marching orders following a rash challenge on Wes Fonguck.
The Bees tried to capitalise on their one-man advantage and could have had their noses in front on 14 minutes when Taylor’s strike from range was well saved by Adam Smith.
Moments later, Johnson’s dangerous free-kick from the right flank missed everyone in the box and almost crept in but the ‘keeper tipped it over the bar.
Barnet’s pressure soon paid off when a delightful ball in from the left by Johnson was nodded home by Robson, giving the hosts a deserved lead.
Taylor tested Smith again from range before Rovers decided to make a double change, Daniel Leadbitter and Stefan Payne making way for Sam Matthews and Kyle Bennett.
The latter nearly made an immediate impact after running through on goal but after letting fly, his effort flew over the bar.
A low shot from Sam Sercombe soon after forced Mark Cousins to get down low and make a smart save to maintain his clean sheet.
Fonguck could have doubled the Bees’ lead just past the half-hour mark but his shot from the edge of the box was well saved.
Rovers thought they had won a penalty minutes later when Tom Nichols appeared to have been tripped in the box but the referee booked the striker for diving. He was then joined in the book by a very animated Darrell Clarke who was shown a yellow for protesting a free-kick awarded to Barnet.
The half ended with pressure from both sides but it was The Bees who entered the break on the front foot.
The visitors had a great chance to equalise in the early stages of the second half. Bennett found himself through on goal but his effort forced Cousins to extraordinarily palm the ball out of harm.
Smith had to race out to block Duku’s shot after he capitalised on a defensive mistake but the ball fell to the feet of Bettamer who failed to bag a debut goal.
The miss proved costly as Rovers clinched an equaliser just past the hour mark. After Callum Reynolds conceded a penalty, substitute Lines stepped up and slotted the ball into the bottom left corner.
However, The Bees nearly regained their lead with 15 minutes remaining after Taylor’s shot from distance bounced off the crossbar.
It was Rovers’ turn to hit the woodwork minutes later after Ollie Clarke’s drive from distance rattled the crossbar via the fingertips of Cousins. The resulting corner then fell to Sercombe who saw his shot cannon off the bar aswell.
Lines came very close to adding to his tally in stoppage time after his sensational low shot struck the inside of the post and out of danger.
The Bees managed to hold on to force a replay which will be played at the Memorial Stadium on Wednesday 21st November.
Barnet Starting Line-up: Cousins, Alexander, Johnson, Reynolds (C), Robson, Adams, Taylor, Fonguck (Sparkes), Sweeney, Duku (Harrison), Bettamer (Walker).
Unused Subs: Matrevics, Tarpey, Coulthirst, Tutonda.
Attendance: 1,705 (523 Bristol Rovers)