Huston, won his third-placed play-off 5-3 against Serbia’s Luca Popovic.
The 20-year-old was watched on by the entire British team, family and local supporters as he reached the latter stages of the knock-outs.
"Having heard the crowd this close to you, that many people all cheering for Great Britain, clapping, hearing them shouting my name was such an amazing feeling," he said.
"I was nervous and the shots weren't as good as I would had liked but I won the match, won the place, and that's all that matters."
Great Britain still has a chance to qualify a women's place, or upgrade to full team invitations in either competition, at the last stage of the 2016 Archery World Cup in Turkey.