The AIL champions got their title defence off to a winning start thanks to a five-minute, first-half blitz which produced three converted tries.
Carlow never really recovered from that punishing onslaught, but did show that they have what it takes to live with the big boys.
Dungannon coach Willie Anderson, having had to surrender his top players to Ulster duty, turned to the continuing development and recruitment process which has served the club so well.
"I think the most important factor was that the players who were at the core of last season's success have carried on what they were doing, and the new players have blended in very well," he said.
"We knew Carlow would be a fairly confident group of players, and they kept going right to the end. But the fact that we sustained our performance was very encouraging, and as we get fitter, we'll play better."
Carlow got off to a flyer with an Ian Dwyer try inside five minutes, but when Jan Cunningham went over after a quarter of an hour, the champions had a 10-5 lead.
And between the 22nd and 27th minutes, the Tyrone men cut loose with some irresistible rugby.
Bryn Cunningham, Tim Barker and Ryan Constable all touched down, with Mark Bradley bringing his conversion count to four.
Dungannon, with the tireless Paddy Johns performing superbly, led 34-8 at the break, and tightened their grip with further tries from Jan Cunningham and Michael Haslett.
Matt Spiller got in for a second Carlow try, but by the time Bobby Baggott scored another for the visitors, Dungannon were beyond reach.
"I'm obviously disappointed at losing, but Dungannon played some great rugby," said Carlow coach Kim Thorbon. "We will learn from that."
SCORING SEQUENCE: 2 mins: I Dwyer try, 0-5; 9: M Bradley penalty, 3-5; 15: J Cunningham try, Bradley conversion, 10-5; 22: B Cunningham try, Bradley conversion, 17-5; 25: Barker try, Bradley conversion, 24-5; 27: Ryan Constable try, Bradley conversion, 31-5; 34: P Jones penalty, 31-8; 37: Bradley penalty, 34-8; 45: J Cunningham try, 39-8; 50: Matt Spiller try, 39-13; 57: Haslett try, 44-13; 63: Baggott try, Jones conversion, 44-20.
DUNGANNON: B Cunningham; J Cunningham, S Mallon, A Redpath, R Constable; M Bradley, K Campbell; R Mackey, N Brady, G Leslie, P Johns, A Kearney, A Boyd, M Haslett, T Barker. Replacements: J Campbell for Leslie, R Mercer for Redpath, P Sandford for Constable, P Curry for Mackey, K Walker for Kearney.
CARLOW: M Spiller; M Buckley, P Jones, R Armstrong, I Dwyer; B Murphy, L Peavoy; P Brennan, J Hannon, L Hannon, E Fitzpatrick, R Bolger, B Baggott, D Hyland, A Melville. Replacements: M Waterhouse for Murphy, R Jones for Peavoy, C Gee for J Hannon, A Treacy for Hyland.
Referee: S Buggy (Leinster)