Initial pressure from the home side failed to yield any points and after 13 minutes, Jordan Case put the first try on the board for Rochdale, the conversion from Paul Crook making it 0-6.
Swinton though continued to apply pressure, forcing a goal line drop out after twenty minutes, with the breakthrough coming just four minutes later when Chris Rothwell made it 4-6 after Jimmy Rowlands failed to land for the extra two points.
A very broken passage of play then led to referee Mr Bloem speaking to both captains and after yet another penalty to Swinton, the Lions scored their second of the afternoon when Grant Beecham went in at the corner, the conversion again missed, making it 8-6.
Less than a minute later, the hosts again through Beecham scored and Atkins again missing the conversion led convincingly 12-6 at the break.
The second half began in much the same vein, both teams testing each other out, before Atkins raced 90 metres to score for Swinton, with Rowland now taking on the kicking duties, with ten minutes gone, it was 18-6.
Rochdale began to give away too many penalties and Rowland again took advantage to convert one of them from bang in front of the sticks to make it 20-6 with just over 25 minutes left of the match.
Rochdale were not going to go down without a fight.
At the very next set, a one-on-one ball steal from Ryan Smith saw Rochdale score their second of the day thanks to James Tilley and another fine conversion by Crook to make it 20-12.
Swinton were not in the mood however to let the visitors steal their thunder, and hit back thanks to more sloppy defending.
When Ryan Smith failed to deal with a grubber towards the corner, Ritchie Hawkyard was on hand to punish the mistake and touchdown an unconverted try with six minutes left.
The Lions were not finished though.
Andy Ackers making a fine break through and finding Atkin in support, who raced away to score his second four pointer of the game.
Rowland’s conversion from in front with just three minutes left meant Swinton booked their place in the fifth round of the Ladbrokes Challenge Cup with a 30-12 victory.
Swinton: Chris Atkin, Shaun Robinson, Stuart Littler, Chris Rothwell, Richie Hawkyard, Ben White, Jimmy Rowland, Mike Morrison, Andy Ackers, Jordan James, Grant Beecham, Rhodri Lloyd, Connor Dwyer.
Subs: Aaron Lloyd, Tommy Gallagher, Ben Austin, Rob Lever
Referee: J. Bloem