Stillingfleet had their lead at the top of division four trimmed by a couple of points by Burn, despite turning in a good performance at Heworth.
Chris Walker and Rob Bielby had Heworth struggling at 12-3, but John Dale, Archie Woodhead and Ed Dale staged a partial recovery.
Three wickets to Brian Murray on his debut had them all out for 130 and 15-year-old bowler Neil Alexander enjoyed a promising debut.
Rob Murray, not to be outdone by his father's bowling performance, struck a fluent 62 and vice-captain Walker also notched 62 as the Fleet sailed home.
The Burn club go from strength to strength as their second team showed when up against bottom team Stockton and Hopgrove.
It turned into a baptism of fire for the Villagers' new skipper, 17-year-old Michael Colinson, as Burn opener Andy Watson reached 100 and with Ady Huetson (62) put on 157 for the first wicket.
Veteran bowler Noel Copper marked his return out of retirement and taking 3-44 as Burn reached 239-6.
Rich Grimes reached 28, Mick Anderson 19, but with batsmen failing to trouble the scorer the result was inevitable.
Ray Adamson taking 4-11 from eight overs as Stockton head back to division five.
Solid batting form the Acomb top order saw them prosper against the University Staff.
Scott Nicholls and Matthew Dickenson both hit half centuries in a second wicket partnership of 109.
Ashley Pike produced a fighting 58 despite a dislocated finger and Indra Ray 42 as the Staff side replied with a lacklustre 151-8.
The win for Acomb relieves the pressure a little in the relegation zone, while casting the Staff a adrift of the leading teams.
Bishopthorpe, put into bat by Heslington, made good use of a firm wicket at Stillingfleet to register 169-8.
Andy Copeland, who just missed out on a half century, and Andy Spence were the leading batsmen.
Bowler Derek Slack needed all his magic to keep Heslington at bay.
Gavin Dickinson, also out for 49, threatened to take control of the game but became one of man-of-the-match Slack's seven victims as the Bishops won by 18 runs.
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