Mitch McCann (50no) and Brett Hampton (41no) also made significant contributions with the bat.
Bay of Plenty grabbed an easy outright victory when they removed Poverty Bay for 130 in their second turn at bat, to win by an innings and 63 runs.
There were plenty of Bay of Plenty celebrations when Tommy Clout took three successive wickets to post an elusive hat-trick and finish his bowling spell with 4/27.
The last Bay of Plenty hat-trick was taken by Amandeep Singh on debut against Counties Manukau in 2006.
Three Bay batsmen are having a real battle to finish the season as the top run scorer. Carter's second century of the season has taken him to the top of the table with 589 runs, just one in front of Hampton (588), with Popli lurking just behind the leading pair with 580 runs for the season.
Fergus Hickey Rosebowl
Poverty Bay 152 (Tony Goodin 5/45, Jono Boult 3/16) & 130 (Tommy Clout 4/27 including a hat-trick, Jono Boult 2/15, Sean Davey 2/22) Bay of Plenty 345/3 declared (Joe Carter 108, Bharat Popli 76, Mitch McCann 50no, Brett Hampton 41no).
Result: Bay of Plenty won outright by an innings and 63 runs.