Ross made another big play on the next possession by stealing the ball from Ayon after DeRozan had knocked it away. But Toronto couldn't score at the other end, giving Orlando 10 seconds to try for the tying basket.
But Redick missed a 3 and Orlando couldn't get another shot off before the buzzer, giving Toronto its first five-game winning streak since Jan. 22-31, 2010.
"It felt good when it left my hand," Redick said of his late miss. "I had a direct line, I was square to the basket. I just back-rimmed it."
Casey said it was too soon to put a timetable on Valanciunas' return. Valanciunas is expected to see a hand specialist over the weekend, but no appointment had been scheduled following the game.
Drafted fifth overall in 2011, Valanciunas played in Lithuania last season before joining the Raptors. He came in averaging 8.1 points and 5.4 rebounds and had started all 28 games to date.
The Magic had 18 turnovers, leading to 17 Toronto points.
"We were trying to be aggressive and did some different things offensively," Orlando coach Jacque Vaughn said. "They did a good job of trapping our pick-and-roll at times."
Orlando rookie Andrew Nicholson made his first career start in place of co-leading scorer Glen Davis, who'll be sidelined four to six weeks after injuring his left shoulder in Wednesday's victory over Washington.
Redick said Davis' absence was felt most in the final quarter, because it forced the Magic to alter their regular finishing lineup.
"What hurt was not being able to go to the lineup that we're comfortable playing with," Redick said.
Nicholson's opening basket at 9:37 of the first was Orlando's only lead of the game.
Toronto led 20-15 after one, the fewest points it has allowed in the first quarter this season.
Ross scored six points in the second but Afflalo had seven for the Magic, who cut it to 42-39 at the half.
DeRozan scored six points in the third, including a jumper during Toronto's 7-0 run over the final 1:23 that gave the Raptors a 71-62 lead heading into the fourth.
NOTES: Toronto held its opponent below 100 points for a season-high seventh straight game. ... Toronto's next game is Dec. 26 at San Antonio. ... Afflalo went 9 for 9 from the free throw line. ... Amir Johnson played for the first time since shaving the Raptors logo into the hair on the back of his head.