With Neil Spragg (63) and Andrew Foulds leading the way, Steeton looked on the way to maximum points as they raced to 232-5 and then picked up the first six Rawdon wickets with only 59 on the board.
But Andrew Doidge (48) and Jake Hodges (38) added 87 for the seventh wicket and Franklin (45no) and James Doidge (38) took Rawdon to within seven of victory with one over left.
Stephen Pearson (4-43) bowled Doidge with the first ball but Franklin dispatched the final delivery with style.
Charlie Swallow followed up a knock of 74 with a spell of 5-35 as Ben Rhydding beat Guiseley by 37 runs.
Otley are the only unbeaten side in the division and replaced Ilkley as leaders when they skittled them out for 108 and Ben Morley (68no) steered them to a nine-wicket win.
Alex Lilley (5-30) had Collingham on the ropes until Toby Jacklin (89) and Sean Aitken (44) helped them set a 207-8 target. But it wasn’t enough, Yasar Ali with 64no and Ross Knellor (56) helping defending champions Beckwithshaw to their second win.
Ed Brown hit five sixes in his 102 in Burley’s 202 but a half century from Ryan Nicholson put Bilton on the way to a four-wicket win. Andy Siddall (60) and Paul Malone (58) top scored in Kirkstall’s 241 and despite the efforts of Jacob Rodgers (73), Pool were dismissed for 223.
Umer Yaqoob’s second five-wicket haul in a row saw Green Lane dismissed for 119 and Alex Fox (78no) clinched the victory to keep Follifoot clear at the top of Division Two.