A first half hattrick of tries from flanker Johan Bardoul had the Steamers ahead 18-10. West closed the gap with a 39th minute penalty.
The Steamers were unlucky to have two tries disallowed. However they deserved their 18-13 lead at the interval.
The Magpies regained the lead with a 44th minute try to captain and flanker Brendon O'Connor from a lineout drive. West converted.
A 57th minute converted try from West after good buildup from the forwards had the Magpies ahead 27-18.
A 62nd minute penalty from the Steamers substitute first five-eighth Dan Hollinshead kept the visitors in touch.
West's 68th minute penalty from 50 metres after the Steamers were pinged for playing a player in the air was the turning point. Another West penalty in the 72nd minute, had the hosts ahead 33-21.
Steamers fullback Te Rangi Fraser sparked a thrilling finish with his 76th minute try.
Scorers:
Hawke's Bay 33 (Richard Buckman, Brendon O'Connor, Ihaia West tries; West 4 pens, 3 cons ), Bay of Plenty (Johan Bardoul 3, Te Rangi Fraser tries; Nick Evemy, Dan Hollinshead pens). HT: 13-18.