Lowry scored 35 points while DeRozan weighed in with 32 as Toronto completed a victory that leaves the best-of-seven series tied at 2-2 with three games to play.
The win continues a remarkable transformation in fortunes for Toronto, who had lost the opening two games of the series heavily to trail 2-0.
The Canadian franchise — playing in its first Eastern Conference finals — held its nerve to hang on for a thrilling win on Monday.
With Lowry and DeRozan in imperious form, the Raptors had surged into an 18-point lead midway through the third quarter.
However, the Cavs rallied superbly through LeBron James, who finished with 29 points, and Kyrie Irving to haul themselves back into the contest.
With just over five minutes of the fourth quarter remaining, the Cavs had wiped out the deficit and taken a 92-89 lead.
But just when it looked as if the Cavs might score a vital road victory — and open up a 3-1 series lead — the Raptors rallied again, going on an 11-3 scoring run in the closing minutes to claim the win.
Defensive giant Bismack Biyombo produced another towering performance near the rim, mopping up 14 rebounds to keep the Cavs at bay.
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