Despite a punchy 35 from opener Chris Lowe, Darwen were always struggling for runs. Heaton's 5-14 included the important wicket of Gareth Cordingley, trapped lbw for four.
And the bowler would have had a sixth victim had not Nigel Robbins scooped a defensive shot away from his stumps to be given out ``handled the ball.''
Darwen's 106-9 from their 45 overs did not look enough for victory but Chorley were soon in trouble themselves at 27-3.
Dave Bonner (1-19) and Andrew Mercer (2-16) did the early damage in impressively tight opening nine over spells.
Heaton's arrival at the crease steadily swung the game Chorley's way and the 69 runs fourth wicket partnership with Richard Grayson (23no) took Chorley within sight of victory. Heaton was brilliantly caught by Jeff Hacking at square cover for 51 and it was left to Grayson to finish the proceedings with a mighty six over long on with almost 10 overs to spare.
Rain wrecked Chorley's hopes of victory over Leyland at Fox Lane on Saturday.
Roland Horridge (46no) and Mark Richardson (42) put on 69 for the fifth wicket as Chorley reached 167-5.
Only 10 overs had been bowled in Leyland's reply when a thunderstorm washed out the match, but not before Chorley's deputy professional Kevin Evans from Nottinghamshire removed his opposite number, the free scoring Neil Rimmer, for a duck. Both teams take two points from the abandoned game.
Darwen's agme against Leyland was also ruined by the weather.
Sub pro Brad Young top-scored for the home side with 57 in a total of 151-7 and Kendal's reply was halted at 53-1.