The Rams looked good going forward as they ran in six tries and while there is still plenty to work on defensively, coach Lee Greenwood was pleased his side were able to get off the mark having pushed York City Knights close last week.
Dewsbury always looked in control after racing into a 12-0 lead in the opening 10 minutes.
It took the Rams little over two minutes to open their account as Adam Ryder drove the ball in and stood up in a tackle to offload and send Tom Garratt crashing over next to the posts, with Paul Sykes adding the first of seven goals.
Harry Smith’s crossfield kick caught the wind and blew into touch and from the resulting scrum, Dewsbury mounted another attack. Sam Day broke from acting half-back and sent the supporting Sykes rampaging to the line for a try which he improved.
The Rams were threatening a third try soon after when Liam Forsyth intercepted a pass close to his own line and set up a brilliant Swinton counter attack.
Liam Paisley and Michael Butt linked on an 80 metre break and although the latter was caught, the Lions moved left and created a gap for Rob Fairclough to score, with Smith converting.
Day drove for the line but was held up between the posts, while Ryder was also tackled close before Garratt drove over on the last but he too was held up by the terrific Lions defence.
Swinton were put on a team warning after conceding six penalties in quick succession and the Rams mounted another attack with Garratt collecting a short pass to crash over for his second try next to the posts, which Sykes converted.
Swinton again responded immediately and after being awarded a penalty, they moved left and created space for Kyle Shelford to score but it was too wide out for Smith to convert.
Swinton forced Dewsbury to drop out three times in the first half and they launched another attack which ended with Forsyth gathering a crossfield kick and looked to have stretched over for a try only to be pulled back for offisde.
Swinton did pull a third try back early in the second half when the impressive Fairclough created a gap for Rhodri Lloyd to score but again it was too wide out for the conversion.
Swinton knocked on from the kick off and after the Rams were awarded back-to-back penalties, Sykes slotted over his fourth goal.
Dewsbury grabbed a crucial 54th minute try as Simon Brown produced a neat offload to send Robbie Ward scrambling over the line and Sykes converted.
Swinton had been put on a second team warning in the build up to the try and were reduced to 12 men when Fairclough was sin-binned soon after the re-start.
Swinton were attacking close to the Rams line when Rob Worrincy intercepted a pass and the winger went on a superb 90 metre run as he outpaced the Lions defence to score a spectacular individual try, which Sykes improved.
Having taken play close to the line, Owen Harrison - on loan from Hull KR - received the ball and spun in a tackle to crash between the posts to give Sykes a simple goal as the Rams led 38-14 with just 10 minutes to play.
Hatton replied with a consolation try when he crashed over at the side of the posts and Smith converted before Lloyd send Butt over in the left corner in the final minute but it wasn’t enough to prevent Dewsbury securing their first win of the season.
Dewsbury Rams: Hooley; Worrincy, Igbinedion, Ryder, Morton; Sykes, S Brown; Annakin, Day, Garratt, Walshaw, Trout, Field. subs: Ward, Knowles, Harrison, Sheriffe.
Swinton Lions: Hansen; Butt, Lloyd, Paisley, Forsyth; H Smith, Fairclough; Bennion, Waterworth, Hatton, Shelford, Halton, Byrne. Subs: Brickhill, P Jones, Partington, A Jones.
Referee: Gareth Hewer