Doncic delivered his best when it mattered in the fourth quarter where he made 15 of his 33 points while Irving had set the tone early with 24 of his 30 points coming in the first half.
Karly-Anthony Towns and Anthony Edwards, the main points threat for the Timberwolves, were limited by the Dallas defense. Edwards had 19 points and Towns had 16 and together they shot 12 for 36 from the field.
Minnesota took a 102-98 lead with 3:37 left in the fourth after a 24-foot three-pointer from Edwards.
Dallas responded with eight unanswered points, P.J. Washington made a three-pointer from the corner and then a step-back jump shot from Doncic made it 106-102.
"We had to work really hard to get this one," said Doncic.
"I think we're known for losing game ones, so we were trying to make a point. But it's only one and we have three more to go," added the Slovenian, who was quick to praise Irving for his contribution.
"He got us going, without him we probably would be down 20 at half-time. I had to help him in the second half so we switched roles this time," he said with a grin.
Irving conceded he had been fired up by the comments from Edwards after the Timberwolves' game seven win over last year's champions, the Denver Nuggets.
Edwards said during a television interview that "I got Kyrie", comments that were noted by the Mavericks star.
"I used it as a motivation. When I was sitting at home and I saw that, it was like just a nod of respect. I knew what type of game it was going to be," Irving said.
"But that was also a no-fear mentality and that's why we love him, so I knew they were going to pressure me.
"But also we knew they were coming off a gruelling game seven and their legs were biting them a little bit tonight," he added.
Jaden McDaniels top scored for the Timberwolves with 24 points and hit six of nine three-point attempts while Edwards had 11 rebounds and eight assists along with his 19 points.
Dallas dominated the battle in the paint 62-38 with Washington and Dereck Lively grabbing seven rebounds each.
Game two of the best-of-seven series will also be in Minnesota on Friday and Irving expects an even tougher battle.
"We know they are going to come in the next game and give us their best shot," he said.
"We just have to be able to match it and stick to our game plan".
