Kristaps Porzingis made his return from injury for the Celtics after missing 10 games with a calf injury during the play-offs.
The Latvian, playing against his former side, scored 20 points including 11 from rebounds.
On a disappointing night for the Mavericks, the Texan side will be looking to take hope from their performance in the third quarter.
“I think in those moments we were playing our basketball,” said Doncic.
“We were getting stops. We didn’t allow them to offensive rebound. We were having fun out there in those moments, and that’s what we’ve got to do more.”
Boston host game two of the best-of-seven series on Sunday.
They are aiming to move clear of the Los Angeles Lakers, who also have 17 NBA Championship titles, and will know that 70% of NBA Finals have been won by the team that was victorious in game one.