The Steamers set piece was solid, with Culum Retallick in his 87th game winning the first six lineouts thrown by Nathan Harris.
Winger Elijah Nicolas, promoted into the team from the Bay Development side, made a great break to slice open the Steelers and Toma dived over for try number three after 27 minutes.
The Steamers scored their bonus-point try two minutes later when top-class first five Dan Hollinshead slotted a clever grubber kick into the in-goal for temporary replacement Te Rangi Fraser to touch down. Hollinshead kicked penalties before and after halftime for a massive 30-5 match-winning lead.
Steamers lock Johan Bardoul was sin-binned after 48 minutes and Counties-Manukau scored through Richard Judd to breathe some life into the contest.
Steamers winger Whaimotu Craft-Chemis showed some excellent skills to score his team's fifth try with a fine individual effort, before Counties Manukau scored two late tries to gain a bonus point.
But this game was over at halftime, with the Steamers good value for the win. They take on defending ITM Cup champions Taranaki in Rotorua this Saturday from 5.35pm.
Bay of Plenty 37 (Chase Tiatia, Shahn Eru, Te Aihe Toma, Te Rangi Fraser, Whaimotu Craft-Chemis tries; Dan Hollinshead 3 cons, 2 pen)
Counties Manukau 26 (Richard Judd 2, Sione Fifita, Sikeli Nabou tries; Jared Page 3 cons) Halftime 27-5.