Carlton, who were relegated last season, were guided to 168-7 by an impressive 90 not out from Iftikar Mahmood.
Mohammed Hafeez (37), Naseem Aslam (26) and Kashif Talib (24) led Batley's reply but they were bowled out for 154 as Mahmood claimed 3-23.
Birstall cruised into the quarter-finals with a nine wicket victory over Northowram Fields.
Danny Busfield returned 4-23 from eight overs, while Paul Blakeley conceded just six runs from eight overs and also claimed a wicket as Fields were restricted to 26-6.
R Lees (40) and M Rushworth (33no) led a revival as Fields reached 147-9 at the close.
Birstall required just 22 overs to complete the victory as Connor Williams (66no) and Vikram Rathour (67no) produced an unbroken 143-run stand for the second wicket.
Liversedge are also through to the last eight after they saw off Spen rivals Scholes by 26 runs.
Zulqernain Haider (50), Imran Dawood (59) and Azhar Chunara (38) helped Liversedge to 223-6, with opening bowler Ben Burkill (3-53) the pick of the Scholes bowling.
Nahim Ashraf (74) and Craig Wood (40) produced a 104-run stand for the second wicket, while Ross Irving (30) also shone but Scholes were bowled out for 197.
Simon Kay claimed 3-38, while Dawood capped a fine game against his former club by claiming 3-47.
Mirfield Parish Cavaliers bowed out as they lost by 35 runs at Methley.
Vic Craven (44) and Steve Bourne (40) led Methley to 179, with Mohammed Shahnawaz, Will Atkin, Anthony Bailey and Iqbal Khan collecting two wickets apiece.
Khan (52) and Ibrar Latif (43) produced a 62-run stand in reply but Craven (4-27) capped a fine game, while Chris Kippax collected 3-30 as Parish were out for 144.
Woodkirk avoided a potential banana skin to reach the quarter-finals of the Barry Winstanley Cup with victory over Wakefield St Michael's A.
Spinner Gary Dawber claimed 3-14 as St Michael's were bowled out for 125 before Gary Close (29no), Makbull Mulla (28) and Ilyas Chunara (23) chipped in to steer Woodkirk home.
Mirfield Parish A slipped to a 97-run defeat to Stanley, who had Rahol Bashir (139) in excellent form, while Liversedge A suffered a similar fate as they suffered a 151-run defeat to Hunslet Nelson.
Kashif Rashid blasted 118 in Hunslet's, 243-8 before Liversedge were bowled out for 92.
Over 400 runs were scored at Hopton Mills, where Buttershaw St Paul's chased down 201 to record a five-wicket win.
Moorlands slipped to a 91-run defeat at East Ardsley.
Dan Pauley (3-37) and Paul James (3-22) bowled well but Ardsley made 226 with impressive knocks from Danny McTernan (42), Duncan Arnolda (38), Rob Hoban (34) and Tom Chester (39).
Moorlands' reply centred around 58 from opener Greg Sheehan but they were bowled out for 135.
Birstall A mirrored their first team's performance with a nine wicket win over Northowram Fields A in the Wheatley Cup first round.
Danny Henry hit 93 not out as Northowram posted 151-4 but an unbroken 132-run second wicket stand between Rob Ellis (79no) and Richard Hobson (63no) saw Birstall home in the 25th over.
Qadir Hafoor smashed 104 as Batley A made 238 against Carlton.
Although Ed Taylor (75) shone in reply, Carlton were bowled out for 179 with Kamran Rashid picking up 3-21.