But some canny changes made by Jeffries at the break, particularly the input from halfback Jonty Wood and Steamers prop Ziggy Fisi'ihoi, made all the difference as the Bay ran in five second-half tries.
Jason Harvey, Fisi'ihoi and Wood scored Bay of Plenty's other tries with Mathew Cole, Tim O'Malley and Mason Walker adding the extras from the tee.
In the other game played at Greerton Park, Bay of Plenty under-19s lost 36-3 to Waikato under-19s in round two of the grading games to find the seedings for next month's Jock Hobbs Memorial Under-19 tournament in Taupo.
Waikato were quickly into their stride with the young Bay of Plenty boys struggling to gain parity up front and to defend for multiple phases against their opponents, who have trained together since November.
Bay of Plenty coach Cory Sweeney says Waikato dominated the set pieces and possession, which gave them the momentum to drive forward on attack.
"They exposed us through the middle of the field and they had a very strong forward pack that managed to get three tries really close to the line," Sweeney said.
"They have been together a long time and a lot of them are full time and getting pretty well resourced. But our boys certainly had fighting spirit. They stayed in it and they showed real passion towards the cause, but I think it highlighted the level that we've got to be at."