Boston appeared headed to a 3-0 series lead, after Daniel Theis slammed home an emphatic dunk for a 103-101 edge with a half-second to go.
The Raptors called timeout, and Lowry fired the inbound over 7-foot-5 Tacko Fall to Anunoby, wide open on the far side of the court.
Anunoby connected on his shot to complete the comeback win.
Game four will take place Sunday.
In the Westen Conference, Kawhi Leonard scored 29 points, and the Los Angeles Clippers rolled past the Denver Nuggets 120-97 in game one of their semifinals series.
Leonard connected on 12 of 16 shots from the floor in 32 minutes, sitting out the fourth quarter. Although his streak of five consecutive games with 32 or more points ended, Leonard has scored at least 29 points in each of the Clippers’ seven playoff games.
He is averaging 32.3 points per game in the postseason.
Paul George contributed 19 points and seven rebounds and Marcus Morris Sr. added 18 points, converting 7 of 10 shots and 4 of 5 3-point attempts for the Clippers. Montrezl Harrell had 15 points and Lou Williams scored 10.
Denver’s Nikola Jokic had 15 points and Paul Millsap finished with 13 points, nine rebounds and three steals.
Jamal Murray, Jerami Grant and Monte Morris chipped in 12 points apiece for the Nuggets, who had just one day off after clinching their seven-game series Tuesday against the Utah Jazz.
Game two in the second-round series will be played Sunday.