A first-time All-Star this season, DeRozan struggled in his postseason debut on Saturday. He went 3 for 13 from the field and scored 14 points in Toronto's 94-87 loss.
On Tuesday, DeRozan eclipsed that total in the fourth quarter alone, scoring 17 of Toronto's 36 points.
''We knew he was going to bounce back from the first game,'' Brooklyn's Deron Williams said. ''He took over the game, hit some crucial shots, some tough shots. We've got to do a better job of stopping him, especially late.''
DeRozan made nine of 21 shots and went 12 for 14 at the free-throw line, hitting nine of 11 attempts in the final quarter.
''He bounced back, refocused,'' Raptors coach Dwane Casey said. ''Making those free throws down the stretch was huge. For him to come through after a tough first game and everyone doubting him, I was really happy with that.''
So was Raptors guard Kyle Lowry.
''Tonight he showed what he can do,'' Lowry said of DeRozan. ''He did an unbelievable job of attacking, being aggressive.''
Amir Johnson scored 16 points and Lowry had 14 for the Raptors, who outrebounded the Nets 52-30. It was Valanciunas' second straight playoff double-double.
''There was no way we were going to lose that game,'' Amir Johnson said. ''It was a must-win for us.''
Joe Johnson scored 18 points, Williams had 15 and Mirza Teletovic 14 for the Nets, who will host Game 3 on Friday night.
''There's a lot of positive things that we've done in these first two games,'' Nets coach Jason Kidd said. ''Now we've got to go home and protect home.''
Hampered by foul trouble throughout the game, Brooklyn's Paul Pierce went 2 for 11 from the field, including 0 for 6 from 3-point range. He finished with seven points.
Pierce was upset that the Nets failed to take a 2-0 stranglehold on the series.
''We had them on the ropes,'' Pierce said. ''Definitely.''
Kevin Garnett scored 13 points and Shaun Livingston had 12 for the Nets, who led 66-64 heading into the fourth and couldn't take advantage of 21 Toronto turnovers.
''They did a better job of executing and we just couldn't stop them,'' Williams said.
Pierce converted a three-point play on his first field goal of the game to tie it at 83 with 3:48 left, but back-to-back jumpers by DeRozan on either side of a missed shot by Pierce gave the Raptors an 89-85 lead with 2:11 remaining.
Garnett cut the deficit in half with a pair of free throws, but Lowry scored a driving layup, and then forced a steal that led to a Patterson foul shot that gave Toronto a five-point edge. Pierce answered with another three-point play, and the Nets trailed 92-90 with 59 seconds remaining.
A turnover by DeRozan gave possession back to Brooklyn, but Pierce missed a 3 and the Raptors grabbed the rebound. DeRozan was fouled and made both with 20 seconds left, giving the Raptors a 94-90 lead.
Joe Johnson made a layup but Amir Johnson replied with a thunderous dunk, delighting the crowd of 20,382. Pierce missed again, DeRozan grabbed the rebound and sealed it with four free throws in the final 12 seconds.
''It's everything you dream about, especially when you become a professional athlete, to be at the highest level and have the trust of your coaching staff and your teammates to have the ball in your hands and win a game for them,'' DeRozan said. ''That's big.''
NOTES: Toronto's 52 rebounds were a playoff record. Toronto had 50 rebounds against Detroit on Apr. 24, 2002. ... Brooklyn matched a team playoff high with 14 steals. ... Casey finished fifth in NBA Coach of the Year voting, well behind winner Gregg Popovich of San Antonio. Casey got five first-place votes, nine second-place votes and 18 third-place votes. ... Toronto mayor Rob Ford attended the game. Ford, who has acknowledged smoking crack cocaine, was showered with a mix of cheers and boos when he was shown on the screen during a stoppage in play.