The Australian struck a superb 108 before dismissing the hosts' top three batsmen with the ball.Â
After their early-season struggles, Portsmouth racked up their third straight win and moved up to sixth in the table.
Skipper Marston feels his side's recent success has been because of the impact Hay and Andrew Marston (five for 18) have made.
He said: '˜Fraser was pretty destructive with the bat and then other people stayed around at the end to make a total they were unlikely to ever get.
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'˜When he is playing and bats more than 10 overs you have quite a good chance.
'˜We were missing a few batters and weren't expectingÂ our highest score of the season.
'˜We always knew when reinforcements came we'd start climbing the table.Â
'˜You can still lose games even with your best players butÂ it's a great start to the second half of the season.'
Meanwhile, Sairsbury Athletic were involved in a rare tie at Liphook & Ripsley.
The hosts notched 276 for eight with Tom Kitcher (three for 72)Â the pick of the away side's bowlers.
In reply, Tom Nightingale scored 83 from just 67 deliveries.
MattÂ Journeaux (44) and Chris Sanders (35 not out) also contributed but Sarisbury finished on the exact same score as their opponents.Â