"I'm very happy with my start to the weekend, " Hamilton told the Formula One website.
Hamilton, who became Formula 1's youngest world champion in 2008, struggled in a poor car at the start of the season.
Smith, music legend Quincy Jones and Formula One driver Lewis Hamilton were among the stars introducing acts.
In Formula One, Lewis Hamilton secured the title only on the last corner of the last race, becoming the youngest ever champion at the age of 23.
Brawn's comments came as reigning Formula One champion Lewis Hamilton also told CNN in an exclusive interview that the loss of big teams such as Ferrari would damage the prestige of the sport.
Formula 1 stars Lewis Hamilton and Jenson Button show up in the video that is part of a slick series detailing the impressions of the drivers as they arrive at the biggest race tracks for competition.
The Jonathan Ross Show - which drew a peak audience of 4.6 million - saw the presenter interview Hollywood actress Sarah Jessica Parker, singer Adele and Formula 1's Lewis Hamilton.
Hamilton, 23, could become the youngest Formula One champion in Sunday's season-ending race.
At the Hungarian Grand Prix in 2009, Lewis Hamilton achieved the first historic victory for a Formula 1 vehicle featuring KERS hybrid technology in the form of the Mercedes-Benz KER System.
ENGADGET: Visualized: Mercedes-Benz SLS AMG E-Cell bares all
Hamilton is also learning that his wonderful rollercoaster of Formula 1 is not just up, up, up - he has to ride out the downs as well.
The FIA president said that Hamilton and Alonso would have been thrown out of the Formula One title race if he had got his way.
Hamilton, who became the youngest driver to win the Formula One world title this year, will also perform a demonstration run in his McLaren F1 car.
Mercedes-Benz shook up the world of Formula One today when it announced that Lewis Hamilton, the most sought after free agent driver in the sport, would join Mercedes next year.
FORBES: Lewis Hamilton In And Michael Schumacher Out At Mercedes
It was another superb performance in the wet from Hamilton, who has inherited Michael Schumacher's mantle as Formula One's rain master.
Meanwhile, Damon Hill, the last Briton to win the Formula One title back in 1996, said he believed Hamilton would eventually win the championship.
Seemingly cruising to fourth or fifth place and the guaranteed Formula One World Championship title, McLaren's Lewis Hamilton was first passed and then forced to pit for wet tires.
Before the Briton entered Formula One last year, Dennis said he would give Hamilton a rare McLaren F1 road car, currently on display at the Woking factory, if he won three titles for him.
AUSTIN, Texas Lewis Hamilton won the United States Grand Prix in Austin, Texas on Sunday, in the first stateside Formula One race since 2007.
WSJ: Formula One: Lewis Hamilton Wins U.S. Grand Prix in Texas
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