Flanker Shahn Eru then crashed over for his first ITM Cup try. The 14-0 lead was reduced immediately from the kick-off with a runaway try by Sione Fifita completely against the run of play.
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 Hollinshead slotted a clever grubber kick into the in-goal and temporary replacement Te Rangi Fraser touched down with ease.
Hollinshead kicked penalties before and after halftime for a massive 30-5 lead. Steamers lock Johan Bardoul was sin binned for foul play after 48 minutes and Counties Manukau scored immediately through Richard Judd.
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.
The Steamers are in action again this Saturday in Rotorua, against defending ITM Cup champions Taranaki 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