Driffield were put in by the hosts and looked set for a heavy defeat after slipping to 8-4 inside three overs as Steven Sergeant (4-27) tore through the top order.
Sam Drury (34) and skipper Danny Broumpton (58no) got them back on track but again they struggled to 94-7 until an excellent unbeaten eight-wicket stand of 112 between keeper Mark Goddard (57no) and Broumpton took them to 206-7 from 38 overs.
Goddard smashed five sixes and four fours in his superb innings.
The Hull reply was limited to just 13.2 overs by which point they had reached 72-2, Tim Appleyard the top scorer with 23.
Scarborough had to fight hard after Jack Murphy (57) and Steve Liburd (29) had got visitors Dunnington off to a bright start at 84-1.
Skipper Ben Elvidge (3-38) and Tom Precious (2-41) struck back for the hosts and when the rain arrived the match was evenly poised the visitors having reached 163-6.