However, it took a huge second-half performance from the Dragons to claw themselves back into the game after they trailed 12-6 at the break following two tries by Lifeimi Mafi.
Former Newport forward Chris Wyatt had a hand in the first try after just eight minutes, driving into the heart of the Dragons defence before Jeremy Manning sent Mafi crashing over from close range with a clever inside pass.
Sweeney pulled back a penalty after missing his first attempt but the Dragons failed to capitalise when Munster hooker Andy Kyriacou was shown the yellow card and Mafi stepped through for his second of the night.
Anthony Foley was back from a long-term injury for Munster and his drive opened space before Mafi stepped through just before half time. Yet the Dragons awoke in the second half and Ringer sparked the comeback with his 48th-minute try, converted by Sweeney for a 13-12 lead.
The Dragons pack regained their foothold in the game after their defence stepped up: teenager Ashley Smith caused British Lions lock Paul O'Connell to spill the ball with his goal-line tackle.
Donnacha Ryan was sent to the sin bin for the final ten minutes, handing Sweeney a penalty in front of the posts to nudge Newport clear. He duly dispatched with ease, before sealing the win a minute from time.