Nick Summerscales's impressive haul of 5-28 bolstered Heaton's aspirations as Bierley were 128 all out.
Opener Gharib Razak (23) and Andrew Rennison (27no) were the only batsmen to trouble Heaton, who had Imran Arif opening the bowling with Summerscales and finish with 2-38 in 13 overs. Chris Schofield did the damage in the middle order, claiming 2-34 from nine overs before Summerscales swept through the tail with four wickets as Bierley folded.
Things didn't get off to a good start as the first three Heaton wickets fell for 11.
Amar Rashid took up the challenge and top scored with 28 but he couldn't find partners to stay with him as the Bierley bowlers got into their stride.
Chris Elstub did most of the damage with 4-24 while Paul Hutchinson (2-21) and Luke Jarvis (2-8) combined to bowl out Heaton for 106 in 42.4 overs.
Heaton's seconds secured a two-wicket win over Spen Victoria.
Peter Byrne (3-36) led the charge as Spen Victoria were bowled out for 134. A Hussein top scored with 34 for Spen.
Howard Ellis (32) and Richard Smith (32) combined to see Heaton to 135-8 in 45.3 overs.