But the Bulls left it very late with both goals coming in the final five minutes, leaving Shrewsbury regretting a number of missed opportunities in the first 45 minutes.
Hereford recalled Gareth Sheldon to the front line in place of Andy Williams and preferred Webb to Richard Rose in midfield as they made two changes from the original tie at Gay Meadow.
Meanwhile, Town included Andy Cooke up front in a bid to pep up their shot-shy attack.
It was the visitors who had by far the better of the first period and what chances there were fell to them.
Neil Ashton should have done better with an opening ten yards out but drove the ball wide of the target.
Ben Davies also failed to hit the target with a good chance, while Cooke headed a Davies free-kick over from a good position.
Towards the interval, Hereford goalkeeper Wayne Brown was called into the action, making good low saves from a Cooke shot and a Dave Edwards header with both chances emanating from Ashton crosses.
As Hereford finally started to get their game together, Webb forced Scott Shearer into his first save of the game on 58 minutes.
Then Phil Gulliver should have done better when Rob Purdie's free-kick broke to him ten yards out.
Unfortunately, the big centre-back snatched at the chance and drove his shot wide of the target.
The arrival of substitute Williams on 67 minutes had the final galvanising effect on the home side.
The substitute was brought down five minutes from time on the edge of the area.
Connell stepped up to curl his free-kick sweetly around the wall and into the corner of the net off the far upright.
But if that was a fine strike, an even better one was to come three minutes later.
Williams raced down the wing and cut inside before pulling the ball back to Webb.
The young midfielder struck his shot from 25 yards first time and the ball swerved well out of reach of Shearer and into the corner of the net.