Allen sank three 3-pointers to go along with a game-high 28 points in a 92-81 victory in front of a sellout crowd at London's O2 arena, the last stop on the Celtics' European tour.
Garnett, a 10-time All-Star and the league's most valuable player in 2004, had only nine points and six rebounds on the night.
The 6 ft 11 ins power forward was traded to Boston this summer in a record 7-for-1 trade after spending 12 seasons with the Timberwolves.
"It's a new team over there, with new faces... but when it comes to (Minnesota), I have no hard feelings," Garnett told reporters.
Minnesota's Ricky Davis led his team with 18 points, 16 of which were scored in the first quarter.
"It was definitely a different experience seeing Kev in green," Davis said of his former team mate.
"I almost threw him the ball, but then I saw him in that green jersey."
The NBA's 12-day Europe Live tour includes seven pre-season games across six cities in four countries.
Minnesota won 84-81 against Turkey's Efes Pilsen in Istanbul on Saturday while Boston beat the Toronto Raptors 89-85 in Rome on the same night.

