Tour de France champion Froome was defending his title Down Under, bidding to become the first rider in more than a decade to claim back-to-back titles in the five-day event.
But the Team Sky man left himself with too much to do on the final stage, which was won by his team-mate and fellow Briton Ian Stannard.
Howson, of the ORICA-Scott team, finished with Froome in the bunch on the hilly closing 121-kilometre ride at the Kinglake National Park, a town north-east of Melbourne.
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Froome, who was one minute and 12 seconds down in the overall standings, paid tribute to the winner, saying: "Damien Howson was really strong. He rode a great stage on Falls Creek and has defended the jersey really well. Chapeau."

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Stannard's stage win was also appreciated by Froome, who said: "He's an absolute beast of a rider. That's the thing about Ian. He's so versatile. He's 85 kilos or something but still wins on top of a climb. It's scary."
Howson, a 24-year-old rider from Adelaide, follows the likes of Froome and Sir Bradley WIggins onto the list of champions in the event.
Quoted on the event website, he said of his success: " I'm really happy to join that list of guys and to get my first win only a couple of days ago to continue all the way through and keep the yellow jersey on the final day, it's my first overall win ever. It's also nice to break into new territory for myself."
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