Coming into the match, Canberra had not won any of their last 14 encounters with the Storm. But they built an early advantage, leading 14-4 at half-time, and withstood two second half tries from Melbourne to preserve the victory.
Three tries (two to Monaghan, one to Carney) gave Canberra a 14-0 first half advantage before Cameron Smith scored for Melbourne virtually right on the dot of half-time.
Canberra scored the first try of the second half through Carney, and looked fairly safe at 20-4 up. But tries to centres Greg Inglis and Will Chambers got Melbourne back to within four with around 15 minutes to go.
However, the Storm could score no further, and Canberra put a cherry on top of their winning cake when Bronson Harrison capped a quality individual game by crashing over in the dying seconds.
Melbourne had a three-game winning streak broken with this loss. Heading into this game, they had only lost once in their previous eight matches, including a 46-4 flogging of the Raiders in Melbourne six weeks ago. Conversely, Canberra had only won twice in their last eight games leading into this contest.
Apart from tryscorers Monaghan, Carney, and Harrison, Canberra were bolstered by good performances from the likes of captain Tongue, halfback Marc Herbert, and big men Tom Learoyd-Lahrs, David Shillington, and Dane Tilse.