But John Randerson's side lost ground on the leaders when Monday's home game against Scarborough was abandoned after heavy rain made the Savile Park strip unplayable.
Put into bat at Cleethorpes, Cas began brightly, with Chris Young and Australian David Murphy (27) putting on 40 for the first wicket.
But when skipper Randerson fell for a duck with the score on 58-4 they were in trouble until Yorkshire all-rounder David Wainwright took charge, hitting nine fours and a six in a 77-ball innings of 72.
And with the tail all making valuable runs, including knocks of 18 from both Will Hodson and Gary O'Neill, Cas made 215-9 from their 55 overs.
Openers Bill Kirby (49) and Ishan Mutaliph (34) put on 65 as the hosts' reply began superbly but Cas stuck at their task and not even a defiant 61 from James Osmond could get Cleethorpes over the line.
Wainwright bagged 3-43 and Young and Hodson snared two wickets apiece to restrict the home team to 204-8 at the close - and earn Cas a six-point return.