Chasing, only 128 by Bierley, Heaton were bowled out for 106.
Chris Elstub did most of the damage claiming 4-24 in 12.4 overs but there were useful performances by Paul Hutchison 2-21 and Luke Jarvis 2-8. Amar Rashid was the only Heaton batsman to show any resistance with 28, the top scorer was the extras, who contributed 35.
Earlier Gharib Razak had opened up with 23 and Andy Rennison was top scorer for Bierley with 27.
Woodlands were involved in another low-scoring game. They reduced Mannigham Mills to 90, led by Richard Spittlehouse with 5-23 and Harry Smallwood 3-23. Pieter Swanepoel chipped in with 2-25.
Scott Richardson opened with 37 for Woodlands, supported by Sam Frankland 20 and Nick Rushworth 24 as Woodlands reached 92-3 in 19.4 overs.
Cleckheaton lost by four wickets to Saltaire.
Ian Nicholson made 53 and was the cornerstone of Cleckheaton's 160 total, Craig Thornton made 32.
Tuseif Arshad claimed 4-54 for Saltaire.
Craig Wiseman 2-46 and John Wood 2-16 did their best to boost Cleckheaton but Saltaire reached their target with four balls to spare.
In Division Two Gomersal secured the lion's share of the points against Keighley. Chasing 154-8 Gomersal reached 155-4.
Gomersal's Kashif Naveed hit four sixes and nine fours in his rapid innings of 78 from 47 balls. He was supported by opener Richard Gould, who made 40.
Spen Victoria struggled at Morley and were bowled out for 70 in reply to the home side's total of 145-5.
Adam Larkin hit an unbeaten 81 for Morley.
Imran Amin was the pick of the Spen bowlers with 2-50.
Spen Victoria's reply never got going particularly as Muhammad Ahzarullah fired in and collected 5-43, Rob Lintin-French was equally lethal, taking 3-7 from his four overs.
Windhill proved too strong for Hartshead Moor as they raced to 209-6, Tahir Amin top-scored with 44.
Simon North was the most effective Moor bowler, taking 4-50.
The Moor batsman were led by opener Graham Hilton with 34 supported by North, who made 29, but it was in vain as they were bowled out for 103 in 41.2 overs. James Pringle did most of the damage with an economical haul of 5-19.