They were made to work hard and the tight nature of the contest was highlighted as Dale Breakwell landed three drop-goals which in the end proved the difference between the two West Yorkshire teams.
But with Heath coming into the game on top of the table with only one defeat from their first seven league matches it was a superb win for Cleck and a tribute to their defensive organisation.
Cleckheaton did manage to breach the Heath line twice with Oliver Depledge and Jack Marshall going over for tries.
Breakwell's first drop-goal came after only five minutes. The visitors then come under severe pressure, but their defending was outstanding and when they ventured into the home half again Breakwell landed his second field goal to make it 6-0.
Even when they went down a man after a sin-binning Cleck remained defiant with only a penalty goal by Chris Johnson putting Heath on the scoreboard before the interval.
The hosts levelled with a second Johnson goal after the break, but found themselves 10 points behind when Depledge scored the first try and Breakwell added the conversion plus his third drop-goal.
Back came Heath with a Johnson penalty then a Jason Merrie try, converted by Johnson, to level again at 16-16.
But Cleck won it when the speedy Marshall touched down in the corner and Breakwell kicked a great conversion.
Next up for fifth-placed Cleckheaton is Ilkley at home this Saturday while Heath, who have slipped to second, are away to Doncaster Phoenix. Kick-offs are 2.15pm.