After P & S had been restricted to 113-5 at Allotment Road, Peach rearranged home skipper Josh Hill’s stumps for a second-ball duck.
Peach trapped wicket-keeper Simon Orr, batting at No 3, leg before - also without scoring - and Athletic were 14-3 when Peach (4-1-10-3) bowled opener Elliot Smith (5).
Jed Bradley (19) and Chris Sanders led a fightback, putting on 37 for the fourth wicket before Matt Williams won a leg before verdict against the former.
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Williams (3-8 off four overs) reduced Sarisbury to 60-6 by bowling Ben Bradley (6) and Will Bolton (0) in quick succession.
Sanders top scored with 36 but P & S held their nerve to win by seven runs as their hosts closed on 105-8.
Earlier, Jack Davies had continued his superb T20 form.
The P &S opener struck an unbeaten 90 in last season’s SPL Plate semi-final win against Rowledge, and improved on that with an undefeated 103 in the final loss to Fair Oak.
In the SPL Cup first round this summer, he struck 83 in a losing cause against Ventnor.
This time Davies hit a run-a-ball 46 - the next highest score was wicket-keeper Ollie Kanavan’s 19 - after skipper Ben Saunders had won the toss and elected to bat.
Sam Hill (2-21) recorded the best Sarisbury bowling figures.
*Babu Veettil played a major role as Gosport Borough failed to spring a Southern Premier League T20 Plate shock.
Up against two divisions higher Andover, Borough were skittled for 65 at Privett Park. Though they superbly hit back to reduce Andover to 54-7, the visitors ended up winning by three wickets in the 15th over.
Veetill (4-16 off four overs) removed Gosport’s top four as they sank to 28-4.
Jacob Harris (17) and Charlie Creal (17 not out) top scored with captain Jack Richards, batting at No 11, the only other man in double figures (11).
Veetill, having opened the bowling for Andover, also opened the batting for them and top scored with 16 before he was bowled by Harris.
Andover looked on course for a comfortable win at 47-3, but Richards (3-15) was the catalyst for four wickets tumbling for 10 runs.
There were no further alarms for Andover, though, who won in the 15th over.