Marty Banks kicked a great goal from 50 metres and added the conversion to a well taken try to Tom Marshall, after barnstorming centre Kieron Fonotia sliced open the Steamers backline.
Banks stretched the Makos lead to 20-10 after a ruck penalty from the kickoff.
Flanker Shane Christie then strolled over from the next play after more mismatches out wide were easily exploited by Fonotia.
Fonotia was in himself a minute later after he charged down a poor clearance from fullback Byron McGuigan to give the Makos a massive 34-10 lead. After the halftime hooter, Steamers hooker Joe Royal scored in the left-hand corner after midfielders Iongi and Doug Edwards combined well.
The Steamers began the second half trailing by 34-15 and scored a rip-roaring try through winger Tino Nemani, after Hollinshead made a sharp break and linked with halfback Kitto.
The good-sized crowd felt a comeback was on and enjoyed Banks missing a simple penalty, but it was short-lived as All Blacks Sevens star Bryce Heem cut through and set up fullback James Lowe for a try.
Hollinshead ignited a sparkling Steamers attack with a kick and regather and replacement Te Rangi Fraser followed up with a trademark break.
From a strong scrum next play, Johan Bardoul crashed over. Hollinshead converted and the Steamers were back within 12 points with 10 minutes to play.
But Tasman finished strongly, running in two late tries to ease home.
Tasman 56 (Quentin McDonald, Tom Marshall, Shane Christie, Kieran Fonotia, James Lowe, Marty Banks, David Havili tries; Marty Banks 6 con, 3 pen )
Bay of Plenty 27 (Mike Kainga, Joe Royal, Tino Nemani, Johan Bardoul tries; Dan Hollinshead 2 con, pen)
