Tonteri, who won silver in slopestyle three days ago, scored 79.75 points with his final jump to finish at 173.75. Sharpe, a Calgary native, was second with 169.50, while Kyle Mack of the United States took bronze with 163.50. It was Mack's second bronze after placing third in slopestyle.
Sharpe, fourth in the slopestyle event last week, executed a switchback side 1260 and a frontside double 1280 nosegrab.
''It feels pretty good,'' said Sharpe, 19, whose older sister Cassie won a silver in the ski slopestyle on Thursday. ''I was happy to land my runs. Those were the best I can do right now after coming off some big injuries. It's a big confidence boost.''
Michael Ciccarelli of Ancaster, Ont., was fifth.
Switzerland's Elena Koenz won the inaugural women's competition with 157.75 points. Merika Enne of Finland scored 148.75 for silver, while Koenz' Swiss teammate Sina Candrian won bronze with 143.25.
Big air, the final event of the snowboard worlds, is not an Olympic discipline but has been part of the men's program at the worlds since 2003.
With files from The Canadian Press