But Athletic failed to produce the goods with the bat as they slipped to a second successive Division 1 defeat.
For Rowledge, who had beaten Portsmouth off the last ball in their curtain-raiser, it was a second straight win that took them to the top of the embryonic table.
Hill claimed 5-23 off eight overs as the hosts posted 207-8 after being inserted at The Hollow.
The left-arm spinner’s previous best figures had been 5-10 in a National Village KO Cup regional final against Liphook two years ago.
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All the Rowledge top order made a start, with Sam Plater (26) the lowest scorer in the top five.
Hill dismissed both Plater and his opening partner Jontie Sebborn (36) before Jake Wish (48), teenager Zak Le Roux (33) and Ollie Baker (27) proved hard to dislodge.
Wish had also been his side’s top scorer against Portsmouth with 83.
In reply, Rawlins and opening partner Jed Bradley were both dismissed for nine before Jack Lovett (57) and Josh Hill (29) led the fightback.
But the Sarisbury middle order didn’t last long as their score tumbled from 97-2 to 129-7.
They closed on 153-9, leaving Rowledge 54-run winners. It was their second successive defeat, having been beaten by 69 runs in their opening encounter with New Milton.