Barnet ensured their name would be in the hat for the FA Cup third-round draw after netting a late equaliser at Rodney Parade.
League Two Newport took the lead just before the interval, but Danny Collinge levelled in the 89th minute to ensure a replay back at The Hive.
Laurie Walker was called into action in the very first minute to stop Jordan Cropper diverting a cross into his own net.
But Barnet kept the ball well in the opening stages and Cropper's long throw-in at the other end almost found Collinge.
Harry Pritchard's header was caught by Nick Townsend on 31 minutes, while Corey Evans was just wide for the home side.
Newport then saw Bryn Morris hit the post but they took the lead two minutes before the break when Shane McLoughlin fired home at the far post.
Bees went close to levelling seven minutes into the second half when Gary Hooper found Nicke Kabamba with a fine pass and he chipped the ball over Townsend, only to see a covering defender clear off the line.
And Zak Brunt forced an excellent fingertip save from Townsend with a shot from the edge of the box just before the hour mark.
Hooper and Cropper made way for Reece Hall-Johnson and Marvin Armstrong midway through the second half,
And the visitors were inches away from levelling on 70 minutes when Hall-Johnson's excellent ball across the face of Newport's goal just evaded Kabamba.
Morris fired over from distance for County on 78 minutes, while Walker denied Omar Bogle when clean through with a great save moments later.
But Townsend produced a great diving save to deny Kabamba an equaliser soon after, before Anthony Hartigan's corner was headed home by Collinge at close range in the last minute of normal time.
Barnet: Walker, Oluwo (Potter 87), Collinge, Okimo, Cropper (Hall-Johnson 67), Hartigan, Brunt, Pritchard, Hooper (Armstrong 67), Kabamba, Kanu.
Unused subs: Coker, Gorman, Stead, Gillmore, Blower, Revan.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here