Jaylen Brown had 34 points for the Celtics, while Tatum added 21 and Baynes had nine points and 11 rebounds.
Game five is tomorrow in Boston before the series returns to Milwaukee.
Patty Mills had an equal-team high five assists as the San Antonio Spurs eased to a 103-90 win over the Golden State Warriors to avoid a clean sweep.
Manu Ginobili scored 10 of his 16 points in the fourth quarter for the Spurs, who extended their western conference series to a game five, as coach Gregg Popovich remained out after the death of his wife last week.
Mills had nine points but also played an important role in defence as Klay Thompson's hot shooting streak came to an end, scoring 12 points at just 25 per cent from the field.
LaMarcus Aldridge had 22 points and 10 rebounds to lead the Spurs, but they were willed to the finish by the Ginobili.
The 40-year-old played in his 217th play-offs game to break a tie with Shaquille O'Neal for sixth in league history and passed Reggie Miller for third in career three-pointers in the post-season.
Kevin Durant had 34 points and 13 rebounds for the Warriors, who can wrap up the series at home tomorrow.
LeBron James scored 32 points as the Cleveland Cavaliers escaped with a 104-100 victory over the Indiana Pacers to make it 2-2 in their hard-fought series.
James added 13 rebounds and seven assists in his 100th career play-offs game with 30 or more points.
Domantas Sabonis top scored with 19 points for Indiana, who travel to Cleveland for game five on Thursday.
John Wall took over down the stretch and finished with 27 points and 14 assists as the Washington Wizards beat the top-seeded Toronto Raptors 106-98 to level their series.
Bradley Beal led the Wizards with 31 points before he fouled out with five minutes to play.
DeMar DeRozan started 0-for-6, before winding up with 35 points, six assists and six rebounds for the Raptors.
Toronto will host game five on Thursday.
- AP
