Captain Neil Spragg (51) and Craig Walton (49) led the way as Steeton reached 233-9 in their innings, reduced to 45 overs by the weather, as Jason Wright picked up 4-69.
But Burley, especially Ed Brown, were up to the challenge. He hit an unbeaten 95 and, with Nick Brook weighing in on 46, they got home with three wickets to spare.
Also in Division One, James Davies (4-29) and John Brough (3-16) skittled out Guiseley for 94, which was only that high thanks to a fighting 35 from number seven Damon Reeve.
But Otley batsmen also had their problems, struggling to 47-4 before Davies came to the rescue with an unbeaten 44 to clinch a six-wicket win.
Ilkley’s decision to add the experience of Dave Pennett to their promoted squad again paid dividends as they overcame last season’s champions Beckwithshaw.
Pennett (29) shared a third-wicket stand of 69 with Jonathan Hughes (71) in Ilkley’s 199-9, then picked up three cheap wickets as the home side limped to 123-9.
Aussie batsman Conor McInerney has settled quickly at Rawdon, following up a debut 61 with 67 before being run out. But only number ten Jake Hodges (17) provided good support and the home side were dismissed for 131.
That looked as though it might be enough when Kirkstall slumped to 26-4 but skipper Andy Siddall (59no) saw them home by five wickets.
Richard Nicholls hit 64 as Skipton notched 190-7 against Green Lane in Division Two.
Opener Phil Atkinson kept the visitors on target as partners came and went and he faced the final ball from Gary Owens needing four to win but was caught by Andrew Fergie to clinch the game for Skipton.
Aussie Jack Young (63) and Shane Marshall (5-40) put in encouraging performances for new-look Thackley (163) but could not stop them going down to Adel by just one wicket.
Sam Lawrence (4-40) finished off the North Leeds innings for 172 with a hat-trick and then top-scored with 39 in Bolton Villas’ reply but still could not prevent the home side winning by 32 runs.
Andy Bailey picked up four wickets as Knaresborough were restricted to 146-8 and skipper Mark Portlock (29) helped his Harden side to 72-3 before a collapse saw them bowled out with only 17 more runs added.
After finishing bottom of the league last season, Silsden now find themselves top of Division Three after opening with two wins.
Sadir Khan hit 80 in their 172 then took 3-25 and, with Iqbal Khan (4-23) and Guisharaz Ahmed (3-21), dismissed Bardsey for 91.
Horsforth have also made an impressive start, Ollie Hardaker (61) the star of their eight-wicket win at Alwoodley (108).
But neighbours Hall Park faltered against Calverley after Tom Simpson (5-43) had limited them to 142. Jamie Chapman (43no) and Dan Hall (38no) clinched a seven-wicket victory for Calverley.
Syed Hashmi (4-10) and William Pearson (3-41) bowled out Menston for 82 and even though Olicanian slumped to 33-6, Sajeed Ijaz (23) steadied them and with Lee Jackson (17no) clinched a three-wicket win.