Fever and Grayling finished second and third respectively in the event at Picturehouse Central in London.
Homelessness charity Crisis was the focus of this year's event. The brief was to come up with a campaign to raise awareness of homelessness and the work Crisis does beyond Christmas.
Agencies had four hours to work on the charity's brief before pitching their concept back to an audience of 350 people and the judging panel in just 10 minutes.
The team from Epoch centred their pitch on amplifying the voices of the homeless through different mediums in a campaign entitled ‘The Voice of Crisis’.
Second-placed Fever created its own estate agency, called ‘Fauxtons’, while third-placed Grayling came up with a campaign to harness the Finnish people's example of ending homelessness, completely.
Creative Shootout founder Johnny Pitt said: "This year has been the biggest ever, and Epoch completely smashed it today, demonstrating real nerve and some serious creative talent over the four hours, and then on stage."
Epoch will work with Crisis to bring to life its winning campaign in 2020, helped by a £10,000 fee prize, with support from a range of partners, including Crisis' existing agency network.
"To end homelessness we need bold solutions, and Epoch gave us that this evening – along with, frankly, all the finalists," added Matt Downie, director of policy and external affairs at Crisis. "The team at Crisis can't wait to get going with Epoch, and it's thanks to The Creative Shootout we're able to fight homelessness, together."