Kleiza added five rebounds and two steals. DeMar DeRozan scored 16 points, while Joey Dorsey added 13 points and a team-high 10 rebounds.
It was the first game of the exhibition for the Raptors, who wrapped up their six-day training camp in Vancouver before heading home to Toronto. Phoenix remained winless in the preseason.
Phoenix guard Steve Nash, a two-time league MVP from Victoria, British Columbia, was limited to nine points in just over two quarters.
The Suns' Jared Dudley scored 10 points while former Raptor Hedo Turkoglu, who was traded in the offseason, scored six points and led Phoenix with eight rebounds.
The Raptors played their first exhibition game in Vancouver, although they faced the Vancouver Grizzlies five times in the same arena between 1995-2000 before the West Coast club was relocated to Memphis, Tenn.
Nash drew the biggest cheers from the fans. But most of the crowd at Rogers Arena supported the Raptors. Fans booed Turkoglu every time he touched the ball - and jeered him every time he committed a foul or mistake.
Both clubs missed several shots and layup attempts in the early going as the lead changed hands eight times. The Suns jumped out to a 15-10 advantage as Nash made a free throw, courtesy of a Toronto technical for a 3-second violation, and then made a jump shot.
But those were the only three points he scored in the initial period, and the Raptors went on a 14-3 run to lead 24-13 after the first quarter. Holding Nash to just two points in the second quarter, the Raptors extended their lead to 55-39 at halftime.
Several Vancouver Canucks players, including Mason Raymond, Mikael Samuelsson, Ryan Kesler and Alex Burrows watched the game from courtside. Darcy Hordichuk, appearing jovial after being traded to the Florida Panthers earlier in the day, was in the crowd and came by at halftime to say a quick goodbye to his former teammates.