But the Raiders may have to count the cost of the victory, after inspirational captain Josh Papali'i and centre Matt Timoko picked up injuries.
Experiencing their equal-worst start to a campaign through six games since 2001, Friday night's result means the Storm (2-5) have lost five games in a row for the first time since 2012.
Canberra centre Simi Sasagi mixed style with substance to power his side to victory, taking intercepts, scoring a try, producing an extraordinary pass to set up an Ethan Strange four-pointer and running for 182 metres.
Despite winning their first match against Melbourne in the nation's capital since 2016, the Storm threatened a boilover when fullback Nick Meaney crossed in the 75th minute.
But some desperate goal-line defence helped the Raiders to consecutive wins and improve to a 3-4 win/loss record, having gone into last round's clash against South Sydney on a four-match losing streak.
After being moved onto the wing, Sebastian Kris was busy with 162 metres and seven tackle busts, while Ethan Sanders posted two try assists.
Melbourne's defence couldn't snap into shape even after coach Bellamy said they should have "gone to the pub" after losing 38-14 to the Warriors last round.
Fullback Sua Fa'alogo was productive (186m, two try assists, one try), while Meaney registered two tries in his 100th game for the club.
Canberra started hot and drew first blood when they moved right and found Sasagi, before Horsburgh scooped up a loose ball and wrestled over the line to double the deficit moments later.
But the momentum swung back in the Storm's favour when Horsburgh conceded a penalty after giving the referee an earful, and Sualauvi Fa'alogo scored.
Will Warbrick and Meaney joined in on the try fest to give the visitors a 16-12 lead.
After halftime, Sasagi took an intercept and stormed downfield before the centre threw a stunning offload to Strange, who dived over.
Timoko grabbed a four-pointer in his first game of the season before Sanders slotted two penalty goals.
Fa'alogo tore through the Raiders' defence before handing it off to a running Meaney to set up a thrilling finish, but the hosts held on for the win.
11°C