Zola is back in management after he was sacked by West Ham two years ago and his late substitution paid off as striker Iwelumo found the net in the 108th minute to see off League Two Wycombe on Saturday.
The Hornets should have taken an early lead when Carl Dickinson crossed from the left but Jonathan Hogg's near-post header flew wide.
However, Wycombe had the better of the first half and came close to opening the scoring when Watford's former Arsenal goalkeeper Manuel Almunia spilled Joel Grant's shot and Richard Logan prodded the rebound wide.
After the break Wycombe midfielder Matt Spring, formerly of Watford, played in Logan but the striker could not hit the target under pressure from Nyron Nosworthy.
For the Hornets, Mark Yeates' cross-shot narrowly missed the target and the winger then crossed for Almen Abdi, whose header flew wide.
But the Championship side got their winner three minutes into the second period of extra time when Matej Vydra charged down the left and crossed for Iwelumo to prod home from two yards.