The Eagles dominated at the Leigh Sports Village, but it was not until the second half that the visitors really came good having trailed 8-6 at the break.
Aston’s men were told in no uncertain terms to raise their games with a firm half-time team talk – and they duly did by scoring 46 points following the resumption for a deserved win.
“We didn’t look great in the first half,” admitted Aston.
“We looked rusty and scratchy – and they (Swinton) took advantage of that.
“We played with confidence in the second half and it was much like our normal selves.
“We scored some good tries and limited them to just a couple,” he said.
“I ripped into them a bit at the break as some of them still had their heads in the cloud. They needed bringing back to earth and to needed to knuckle down to the task.
“It was a great playing surface and the facilities are one of the best, so if you can’t play on a perfect pitch there are no excuses,” said Aston.
“We have a difficult away trip next week so we will need to kick on from this win.”
Ryan Shaw gave the Lions an 11th minute lead with a well-taken try and kicked four successful kicks.
Ben Currie also bagged a brace of tries, but the Eagles were too strong with seven different scorers on the try sheet.
The impressive Dominic Brambani scored two tries and kicked eight successful conversions, with two tries from Tom Armstrong and further tries from Michael Knowles, Jack Howieson, Andrew Henderson, Matt Garside and Pat Smith on target.
Swinton Lions: Hawkyard, Burke, Shaw, Clarke, Ballard, Mendieka, Watson, Morrison, Dwyer, Holland, Currie, Bridge, McCarthy. Substitutes: Smith, Mills, Hawkyard, Barlow.
Sheffield Eagles: Lalau-Togagae, Turner, Yere, Armstrong, Taulapapa, Smith, Brambani, Howieson, Henderson, Stringer, Knowles, Green, Szostak. Substitutes: Davey, Roche, Straughier, Garside.
Referee: G Hewer (RFL).