Batley can now start planning for games against Super League champions Leeds Rhinos, Huddersfield, Hull KR and Salford after qualifying for the middle eights stage of the competition.
Batley ran in 11 tries to tame the Lions in front of a huge following who made the trip to Heywood Road for the Bulldogs’ biggest game in years.
The large travelling support was silenced by Shaun Robinson’s fifth-minute try which Chris Atkin converted before Batley stormed back in style with four tries in 10 first-half minutes.
Keegan Hirst was held by the posts before hooker Alistair Leak spotted a gap and dived over from acting half-back, with Pat Walker converting to level matters.
Two minutes later Batley were ahead as Brad Day burst through to set up an attack before they moved left and Walker sent Chris Ulugia over in the corner.
Batley were on a roll and having forced Swinton onto the back foot, Dominic Brambani’s inch-perfect kick was gathered by Wayne Reittie to crash over wide on the right and Walker added a fine touchline goal.
Walker was also on target with a penalty after Lions loose-forward Andy Thornley was sin-binned.
Leak took the ball from acting half-back and raced through a gap to grab his second try, with Walker’s conversion extending the Bulldogs lead to 24-6.
Shaun Squires then leapt to gather another superb kick by Brambani to crash over for Batley’s fifth try, which Walker improved.
Alex Bretherton produced a magnificent try-saving tackle to deny Lions centre Macauley Hallett but Swinton did reply before half-time with a Mark Barlow try which Atkin converted.
Batley put paid to any hopes of a Lions fightback with two tries in the opening six minutes of the second half.
Shaun Ainscough hacked a loose ball on and then sidefooted it inside for Ulugia to gather and race over unopposed, with Walker converting.
Dave Scott was tackled short before Day powered over for Batley’s seventh try.
James Brown raced over after Tom Lillycrop was tackled just short of the line as Batley extended their lead to 46-18 before a further five tries were scored in a dramatic final quarter.
Swinton grabbed a third try when Ben White broke through and found Thornley in support to score by the posts, with Atkin converting, only for the Lions to be reduced to 12 men for a second time when Barlow was sin-binned.
Batley capitalised on the man advantage as they created space out wide for Ainscough to race over in the corner and bring up the half century, with Walker again converting.
Lions scrum half Matty Beharrell raced over at the other end, with Atkin converting but Batley emphasised their dominance by scoring two further tries in the final three minutes.
Ainscough showed great skill to beat his opposite number on the outside to grab his second try in the corner.
Batley then rounded off an excellent display when Brambani gathered a kick and danced his way to the line and Walker added his ninth goal to complete victory before captain Hirst led his side over to the large travelling support to kick-start jubilant celebrations that went on long into the night.
Swinton Lions: Atkin; Robinson, Littler, Hallett, Hughes; White, Beharrell; Lever, Waterworth, Hand, Dwyer, Lloyd, Thornley. Subs: Austin, Bracek, Barlow, Johnson.
Batley Bulldogs: D Scott; Reittie, Squires, Ulugia, Ainscough; Walker, Brambani; Hirst, Leak, Rowe, Day, Bretherton, Gledhill. Subs: Davey, Lillycrop, J Brown, Harrison.
Referee: Scott Mikalauskas.
Elsewhere in the Championship, Dewsbury Rams crashed 58-0 at Leigh, and in League 1, Hunslet edged out visiting London Skolars 30-26.