Allen pumped in 16 of his 20 points down the stretch as Miami equaled the second-longest winning streak in NBA history.
The run tied the Houston Rockets' 2007-08 streak, and the Heat now trail only the 1971-72 Los Angeles Lakers' all-time mark of 33 consecutive wins.
Chris Bosh contributed 18 points against his former team.
Rudy Gay netted 27 points for Toronto, which fell to Miami for the 11th straight time.
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