Willie Anderson watched his side run in six tries, including a Jan Cunningham hat-trick, and insisted it could have been 10. Palmerstown finally buckled under the intense pressure of a swashbuckling performance.
A nervous first-half performance saw the home side concede two tries, the first to Romanian winger Mihai Vioreanu, after home full back Bryn Cunningham had raced clear of the cover to grab the first of his side's six tries.
Earlier, David Humphreys and Damien McCabe had exchanged penalties, and with the scores locked at 10-10, Jan Cunningham swooped for a try.
DLSP kept themselves in contention with a try on the stroke of half-time from Philip Costello, but Dungannon's free-spirited second-half performance overwhelmed Palmerstown.
Scoring sequence: 15 mins: Humphreys pen, 3-0; 20: McCabe pen, 3-3; 23: B Cunningham try, Humphreys conv, 10-3; 30: Vioreanu try, McCabe conv, 10-10; 34: J Cunningham try, Humphreys conv, 17-10; 35: Costello try, McCabe conv, 17-17; 50: J Cunningham try, 2217; 53: Howe try, Humphreys conv, 29-17; 70: Constable try, Humphreys conv, 36-17; 40: J Cunningham try, Humphreys conv, 43-17.
Dungannon: B Cunningham; J Cunningham, R Constable, J Bell, T Howe; D Humphreys, S Bell; J Fitzpatrick, N Brady, G Leslie, P Johns, A Kearney, M Boyd, M Haslett, T McWhirter.
DLSP: E Devitt; P Costello, S Stephens, D McCabe, M Vioreanu; S Broughton, B Hogan; C Condron, S Sarsfield, D Masters, R Frost, P McDonnell, D O'Brien, S O'Donnell, A Wood.
Referee: B Smith (Munster).