However, the home side restored their two-goal advantage before the break, as debutant Mark Quayle gratefully received a poor clearance from Paul Musselwhite to make it 3-1.
Quayle capitalised on a Shaun Smith error to get his second of the night, before Webb converted a penalty after being brought down in the box midway through the second half but it wasn't enough as Boro finished 4-2 winners.
City line-up (4-4-2): Musselwhite; Regan, Whittle, Smith, Holt; Russell, Burton, Fry, Peat; Donaldson, Webb.