Cummings stretched Tiger's lead to 145-142 before Stedroy Baker brought them back to a single point six seconds from time. It was Derby's third overtime defeat of the season.
Derby's coach, Steve Tucker, still missing his injured American, DeRon Rutledge, said: "This was a tough one to bite on. I told my guys we didn't lose this game, the clock just ran out on us.
"Bracknell is the toughest place to play at in the league. Both teams had an iron will to win, but Bracknell were at home and the ball ran their way."
The scores were tied on 87 points each at full-time and then on 101, 117 and 132 after the first three extra five-minute periods. Tiger's Tony Holley led the scorers with 49 points ahead of 41 by Derby's Ted Berry.
London Towers, who played in the previous longest league game against Doncaster Panthers two seasons ago, stay top of the table after their 89-76 win at Worthing Bears. Worthing's injury-jinxed American Shawn Swords was taken to hospital before half-time with an eye injury.Reuse content