Buccaneers maintained their four-year unbeaten run at Ballinasloe on Saturday to leapfrog over the visitors in the league on a heavy pitch, not helped by early morning rain.
The duel between the packs was the main feature of the game with the renowned Buccaneers eight coming out on top.
It was left to the unerring boot of winger Conor Kilroy to account for all the winners' scores, landing two penalties in the opening half and three on the resumption.
Scorers: Buccaneers - C Kilroy (5 pens); Dungannon - T McWhirter try; M Bradley pen, con.
Buccaneers: R Lee; M Devine, A Molloy, M Deane, C Kilroy; O Cobbe, S McIvor; J Screene, J McVeigh, M Cahill, G Webster, R Keady, Des Rigney, E Brennan, M Steffert. Replacements: S Allnut for Molloy, N Rusk for McVeigh.
Dungannon: J Cunningham; A Hood, Alistair Clarke, A Redpath, T Howe; M Bradley, S Bell; J Fitzpatrick, Allan Clarke, G Leslie, P Johns, C Simpson, J Patterson, A Boyd, T McWhirter. Replacements: P Curry for McWhirter, N Brady for Bell, A Blair for Allan Clarke, R Stafford for Patterson.
Referee: O Trevor (Munster Branch).