Without a win in their first 10 matches, the Sheffield club opted to field and restricted hosts Cawthorne to 165 in their 50 overs.
It looked like the visitors would be chasing a higher score when Taruwar Kohli (29) and Liam Wiles (52) added 54 for the third wicket but it needed a last-wicket stand of 39 between wicketkeeper Luke Bullingham (20) and Aaron Feroz (14no) to get them past 150.
Hallam also had a half-century partnership – 55 for the fourth between Joe Cooper (26) and Robert Basu (61) – and kept their heads to win by three wickets with two balls to spare.
Third-from-bottom Tickhill also defeated second-placed Wakefield Thornes.
Tickhill won the toss and opener Mark Cummins’s 37 from 122 balls meant that others had to inject the impetus.
Wicketkeeper Joe Billings took the hint with 39 from 57 deliveries, as did Ross Diver with 26 off 44, but Josh Court was the main aggressor with 29 not out from just 15 balls as Tickhill scored 188-7, with Imran Mahboob taking 4-48.
It looked like Thornes had the edge when Matthew Jordan (50) and James Rhodes (41) put on 88 for the fourth wicket but opening bowlers Royston Dias, who took two wickets in his second spell, and Cummins (2-31) helped Tickhill restrict them to 183-8 and to a five-run win with a combined analysis of 5-80 off 30 overs.
Elsecar almost made it a hat-trick of upsets but lost by one run to Sheffield Collegiate, which was tough luck on Kashif Naveed, who made 75 in the losers’ 200-9, Henry Eldred having made 76 in Collegiate’s 201-6.
There was also last-ball excitement in Yorkshire Premier League North, where Jordan Caley gave Driffield a one-wicket victory over Stamford Bridge by smacking the final delivery for six.
Overseas player Randeera Ranasinghe made an immediate impact for Driffield, taking 4-41 as the hosts were bowled out for 159 (Jack Timby 38, James Pick 37), with Nicky Johnson taking 3-47.
Teenage opener Noah Kelly (42) almost saw Driffield home, being ninth out at 156, setting the stage for Caley, but Will Robertson almost took Stamford Bridge to victory by conceding just one run from his last 17 deliveries.
The contest between the top two at Common Lane did not disappoint, with visitors Castleford making 171-7 after being sent in by Dunnington.
Connor Hyde (35) and Christopher Briggs (41) put on 62 for Castleford’s fourth wicket but both were dismissed by Jonathan Anderson (5-51).
With no David Wainwright in their ranks, Cas slumped to 82-8 but were nearly taken to an unlikely win by Matt Beckett (44) and Dave Brent (24no), who put on 69 for the ninth wicket, only for Hyde (4-44) and Matthew Rees (3-41) to wrap up the tail and seal a 16-run victory.
The Bradford Premier League season is halfway through and Woodlands lead the way by 13 points after another important triumph.
Title rivals New Farnley could only make 173-9, despite 48 from Lee Goddard and 41 from Steve Bullen, and in-form opener Sam Frankland helped Woodlands to a five-wicket victory with 82, Scott Richardson chipping in with 34 not out.
Winless Batley are relegation favourites but they can take pride in their display against Townville, only losing by five runs.
Harry Warwick (65), Conor Harvey (57no) and Jonny Booth (48) contributed to Townville’s 241-5 but the home side were sweating after Abdul Wahid (49) and captain Roheil Hussain (71) put on 111 for Batley’s first wicket, and they ended up just short on 236-6 as Kasir Maroof (32) and Adal Islam (44) carried on the openers’ good work.
James Stansfield (77no) was Moorlands’ hero as they beat title-chasing Hoylandswaine by three runs in the Huddersfield League Premiership, while Airedale & Wharfedale League leaders Saltaire had to show a different side of their character, recovering from 16-5 to graft out a three-wicket win in a low-scoring match against Olicanian.