This was uncharted territory for King who is also the first player from Barbados in the 41-year history of the tournament.
King, who had to go through the qualifying rounds to get into the tournament, is making just his second appearance in the main draw of an ATP Tour event.
He hammered four aces, won 75 percent of his second-serve points and had no double faults in Tuesday's 66 minute match between the two 24-year olds.
"Playing against Bernard, the No. 5 seed is a dream come true," King said.
"The discipline in Barbados is not as big so to come from there and compete against these guys, it's a lot of progress. I'm glad to get my first ATP win.
"I played at least three years in Futures against college guys and Americans then basically had my first breakthrough in Cali, Colombia, in a Challenger against former top 50 player Victor Estrella [Burgos]. Then I realized I can play."
King booked a second round match against Steve Darcis of Belgium who beat Radu Albot 7-5, 3-6, 6-4.
Australia's Tomic had one double fault and won just half of his second serve points.
Earlier this year, Tomic reached the third round of the Australian Open and the quarter-finals of this event two years ago.
In other first round matches Tuesday, Tomic's fellow Aussie Matthew Ebden rallied to beat Canadian qualifier Peter Polansky 6-7 (4/7), 6-3, 6-1 and American Ryan Harrison eased past Russian Konstantin Kravchuk 6-3, 7-5.
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