Fearnley and no.4 Taye McGuinness (12) shared the Bay's biggest partnership of 35 for the third wicket.
In the Hutt innings, Boyle, at 3, topped all scorers with 41 off 64 balls before being bowled by Fearnley, who took 3-1 from 3.5 overs.
Fellow seamer Taylor Scott claimed 2-15 off three, workhorse medium-pacer Tom Rouse 1-7 off four and leg-spinner Jett Whitaker 1-15 off 2.
Hutt reached 106-8 in 26.5 overs for the win.
Hutt coach Mike Nyberg was impressed by the resilience of the Poverty Bay team.
His opposite, Andrew Scott, said that having PB operations manager Nicholas Hendrie and junior development officer Bruce Kerr present on days one and two of the four-day campaign was much-appreciated.
Poverty Bay today play 30-over games against Onslow White and Collegians Black.