The Premier Division high-fliers survived a few anxious moments - twice trailing in the first half - to beat lower division Infinity 4-2 at the PMC Stadium last night.
Tommy Scutt (2), Jamie Clark and sub Harvey Welham were on target in an entertaining second round tie.
It was 2-2 at half-time and remained that way until Scutt converted an 82nd minute spot-kick.
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Welham - one of three 16-year-olds introduced off the bench in the second half alongside Joe Tyrell and Owen Pelham - added an even later fourth.
Another 16-year-old, goalkeeper Bayley Neil, played the 90 minutes - as he had done in a Hampshire Senior Cup win at Brockenhurst last month.
Boss Wilkinson said: ‘In the first half we were a bit slow, a bit sloppy. To be fair, Infinity had a real go at us in the first half.
‘But in the second half we moved the ball better, we dominated - I don’t think they got out of their half. Fitness told in the end.
‘The young lads are only 16 - they’re not 17 for a while. I’ll have no hesitation in using them again.
‘It’s all about managing them, you can’t throw them in all the time - but some are getting close to making the first team squad (for Wessex League games).’
Infinity had twice led through Jamie White and Joe McLean and boss Wayne Grant - in only his second game in charge - was taking the positives.
The former Paulsgrove manager had overseen a 2-1 Wessex 1 win at Whitchurch in his opening match, and last night made six changes (Baffins also made six).
‘It was good,’ he declared. ‘The performances have been improving in the few weeks I’ve been there.
‘It’s a transition time for the players. They’ve been used to playing a certain way and now it’s a blank canvas again.’
Infinity are looking stronger now White - a prolific scorer in the Hampshire Premier League in recent years - has recovered from injury and ex-Fareham Town regular Wayne Boud is available again after a long suspension.
Kurt Watts, once of Gosport Borough, is also back from injury.
Grant hasn’t brought in any new faces yet, but that should change in the coming weeks now he and assistant Lee Jones have had a good look at the squad they have inherited.
‘We like a high press, we like to get the ball down and play. We play to our strengths, I want the players to believe in our game plan.’
Infinity host a Waterside derby against second-from-bottom Fawley this Saturday, while Baffins host Andover Town in the first qualifying round of the FA Vase.