Harvick, who started 24th, led just one of the 200 laps around the 2-mile oval.
Johnson finished second and Busch was third, spoiling his chance to pull off the NASCAR weekend sweep two weeks in a row.
Two-time defending series champion Dario Franchitti won IndyCar's season opener in St. Petersburg, Fla., showing he's once again the one to beat in open-wheel racing.
Franchitti grabbed the lead early on and was hardly challenged in the Honda Grand Prix of St. Petersburg. The Scottish driver was nearly perfect for 100 laps on the scenic, 1.8-mile street course, beating pole-sitter Will Power to the finish line by more than seven seconds.
Tony Kanaan, the 2004 series champion who joined his new team Monday, held off Simona de Silvestro over the final few laps for third. De Silvestro enjoyed her best finish in 18 career starts.
Danica Patrick was 12th, a disappointing start to her seventh IndyCar season. Patrick, who drove four races in NASCAR's second-tier series before resuming her full-time IndyCar gig, was penalized one spot on the final lap for making "avoidable contact" with JR Hildebrand.
It was Franchitti's first victory - and fifth top-five finish - in six starts at St. Petersburg.
Red Bull's Sebastian Vettel opened his Formula One title defense by driving a flawless race and beating McLaren's Lewis Hamilton to win the season-opening Australian Grand Prix in Melbourne, Australia.
Starting from the pole, Vettel maintained his lead after the first turn and had already opened a gap of more than two seconds over Hamilton following the first lap, and the German's lead was never seriously threatened.
Renault's Vitaly Petrov was a surprise third, claiming his first podium finish with a strong showing.
Fernando Alonso finished fourth, while Australian Mark Webber was fifth, as both used three-stop strategies - one more than the podium finishers.
McLaren's Jensen Button was sixth, falling short in his bid to win the race for a third straight year.