Chellew finished with career-best figures of 7-3 from his seven-over burst to play chief destroyer as the visitors were rolled for just 57.
Chris Wood (58 from 114 deliveries) and Tom Abell (81 from 78) then combined for an unbeaten 128-run partnership that secured the Port Boys first-innings points.
The hosts declared at 2-160 to give their bowlers a second crack at Mt Lawley’s batsmen.
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Veteran quick Jamie Heath soon got the better of Oliver Mouchemore, removing the opening batsman twice in one day for a total of two runs from 27 deliveries.
When Ben Moore had Callum Taylor out for eight, a second collapse looked on the cards.
But James Newman (29 from 71) and Corey Evans (seven from 39) steered the visitors to the end of day one.