Rotterdam-born Sluiter was hoping to celebrate the event's 30th anniversary in style, but Mirnyi gatecrashed the party and snatched the trophy and the $154,000 winner's purse for himself.
"It's a big honor for me to join the winner's circle here," said Mirnyi, who was cheered on by his doubles partner, Roger Federer, from the stands.
Mirnyi is the first Belarussian to win an ATP singles event.
"I'm looking forward to coming back here and seeing my name join the others on the billboard at this arena," the world No. 46 added.
Mirnyi said he hoped his win would help win back the support of Belarussian President Alexander Lukashenko, who has turned his attention away from tennis.
The 1.96-meter Mirnyi had not won back-to-back matches since falling to Andre Agassi in the U.S. Open quarterfinals last September.
But Myrnyi gradually drowned out the frenzied support for Sluiter with an onslaught of thundering serves and deep, penetrating groundstrokes.
Having knocked out former champion Yevgeny Kafelnikov and second seed Federer in the previous two rounds, the towering Mirnyi was in no mood to let his chance of victory slip and rarely allowed world No. 72 Sluiter to gain the upper hand.
Sluiter earned the only break point of the opening set in the first game of the match, but it was Mirnyi who rattled off the winners to run away with the tiebreaker 7-3.
Mirnyi dug his claws deeper into Sluiter in the second, claiming the break in the fifth game, when Sluiter hit a running forehand into the net.
The 25-year-old Belarussian stepped up the pace and clinched victory with his seventh ace of the match.
Mirnyi said he hoped that Lukashenko, who was a staunch fan of tennis for many years, would now give more support to the sport.
Lukashenko turned his attention to ice hockey following the national team's surprise run to the semifinals of the 2002 Salt Lake City Games.
"Prior to our hockey team's success at the Winter Olympics, our president backed tennis a lot and used to come to watch events like the Davis Cup," Mirnyi said. "He built a lot of clubs and tries to promote sport in the country, but he now follows hockey a lot.
"However, I'm sure that my success here will bring a lot of interest to tennis in Belarus, and he'll be backing us again."
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