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The Lions crossed for five tries meaning they've now scored 16 tries in just three games to start the season with bonus point wins.
The victory moved Wellington nine points clear at the top of the Championship table.
Young Wellington hooker Asafo Aumua turned in another standout performance, scoring a try and led the attacking stats with nine defenders beaten and 81 metres made.
Wellington opened the scoring in the sixth minute when Malo Tuitama got on the end of an overlap to score a simple try.
The visitors extended the lead six minutes before the break when Brad Shields took a quick tap penalty and recycled the ball to Isaia Walker-Leawere who forced his way over to make it 12-0 halftime lead.
The Steamers finally got on the board with a Mike Delany penalty eight minutes into the second half but Wellington continued to control the game when Ben Lam chased down a Jackson Garden-Bachop chip into the corner for a try.
Bay of Plenty offered some slim hopes of a comeback when Terrence Hepetema scored in the 63rd minute with a Delany conversion closing the gap to 17-10.
However Wellington dominated the closing stages of the match with Wes Goosen and Aumua both scoring to guarantee a bonus point victory.
Wellington will look for four straight wins when they host Hawke's Bay on Wednesday while the Steamers look to bounce back in Palmerston North next Friday.