Struggling Galwegians opened their win account at the fifth time of asking, overhauling Dungannon for a pride-restoring 28-24 success at Crowley Park.
Ulster prospect Peter Nelson scored a try and kicked two conversions as Dungannon took a 24-13 advantage early in the second half, with the bonus point also secured.
Justin Fitzpatrick's charges had settled quickly and right winger Conor Gaston outpaced the Galwegians cover to score a fifth minute try which Nelson converted.
Nelson was then up in support to finish off the visitors' second try just minutes later. 12-0 down, it was 'Wegians' cue to get their game in gear.
Excellent out-half Tadhg Leader landed a penalty before John Cleary glided through from full-back for a sublime solo try, arguably the best seen at Ulster Bank League level so far this season.
Leader added the extras but 'Gannon swept through for their third try before the interval, with number 8 James McMahon getting over for the score.
Scrum half Michael Kirkwood then darted down the blindside for a well-taken bonus point try and when Nelson converted to take their tally to 24 points, the Tyrone side were odds on to take the win.
But ‘Wegians showed their mettle by hitting back with tries from Ivan Muldoon and Connacht scrum half David Moore, amid a fantastic spell of play from their forwards.
Leader continued to kick well, taking his personal haul to 13 points and giving the Sky Blues enough of a lead to see out this vital result.
Referee: Darragh McCormack (IRFU)