Third-placed Deepings fought back from an early setback to claim the derby-day honours.
Bourne, who slipped to fifth after their heaviest league defeat this season, took the lead with a converted try.
Deepings responded well to leave Bourne coach Dave Maudsley feeling frustrated.
He said: “The first half was pretty even but overall they were better than us.
“All season we’ve competed in league games and we hadn’t lost by more than nine points.
“But Deepings gave us a proper hiding on Saturday. We got bullied in the forwards and we lost scrums, lineouts and turnover ball.
“It was hard to get back into the game. I’m disappointed with the performance.”
Deepings coach Nobby Coupland added: “We had a player sin-binned in the first half but we took advantage in the second period playing with the wind.
“We capitalised on Bourne having their prop sin-binned and one of their players got a red card after the final whistle.
“We’re now clear in third and still unbeaten at home.
“We played the majority of the away game with 14 men but this time we made changes for the better.”