The rebuilding San Antonio Spurs stunned the Sixers 114-105 in Philadelphia, where frustrated 76ers coach Doc Rivers said after the game his team was "not ready" to win yet.
In Orlando, Tatum's exploits and a 27-point contribution from guard Derrick White helped the Celtics notch another win in a game that featured 21 lead changes with neither team able to build a double-digit advantage.
Orlando big man Wendell Carter knotted the score at 111-111 with a put-back dunk with 4:23 to play.
Carter then fouled Tatum and Tatum's two free throws ignited a 10-2 scoring run that put Boston up for good.
Terrence Ross led the Magic with 29 points and top draft pick Paolo Banchero added 23, but Orlando fell to 0-3.
That's also where the 76ers found themselves after the inexperienced Spurs -- whose championship chances were downplayed by none other than coach Gregg Popovich before the season -- drained 16 three-pointers on the way to their second straight win.
Devin Vassell scored 22 points, Keldon Johnson added 21 and Tre Jones chipped in 17 for San Antonio while Doug McDermott made four three-pointers on the way to 14 points.
San Antonio's top-scoring trio all have less than three years experience in the league, and Popovich said he was impressed with the young team's performance on the second night of a road back-to-back.
"What it showed me was they are serious about getting better and knowing what the league is like," Popovich said.
The Spurs withstood a 40-point performance from Philadelphia's star big man Joel Embiid but held James Harden to 12.
"We're not ready yet," Rivers said. "Honestly, we're just not. We're not ready to win yet. You can feel that and so we've got a lot of work to do.
"It's almost like we played these first two games hard, competed, and then felt like 'OK, now we can win some games' -- you've still got to go out and earn the game."