Yorkshire county player Alex Lees scored 223 on his Hawke Cup debut a fortnight ago but he fell for four to begin a major collapse.
Joe Carter was skittled first ball, Ben Musgrave and Tim Clarke were both out for second-ball ducks, MacRury fell for 25 and Sean Davey for two to leave the Bay in terrible trouble at 54-7.
Dudding had 6-15 but no one told Deeble it was a lost cause. Fresh from his maiden century for Bay of Plenty against Counties Manukau in the opening Hawke Cup defence, the allrounder got stuck into the bowling and hit Dudding out of the attack.
Deeble's 61 came off 61 balls and included six fours and one big six. He put on 85 with Thompson, who batted 139 minutes for perhaps the most important 45 runs he has ever scored. His partnership with number 11 Chris Atkinson produced another 30 vital runs.
Bay of Plenty's total of 170 began to look decidedly useful as the pace bowlers got stuck into the Hawke's Bay top order.
Deeble, Davey and Atkinson took two wickets each with Tony Goodin unlucky not to join them. Schmulian will be the key wicket on day two if Bay of Plenty are to get a first innings lead.
Hawke Cup challenges played on flat decks like Bay Oval are usually decided on the first innings but this game is so well advanced it may end up being an outright result either way.
Bay of Plenty 170 (Donovan Deeble 61, Brenton Thompson 45, Tom MacRury 25; Liam Dudding 6-46) lead Hawke's Bay 70-6 (Brad Schmulian 28* ; Deeble 2-12, Sean Davey 2-15, Chris Atkinson 2-25)