Win at the Emirates Stadium on April 26 and Chelsea could be crowned champions at Leicester three days later.
The Gunners would have five games to play, but the Blues would have an unassailable 16-point lead and clinch the self-proclaimed Special One's third English championship following his successes in 2005 and 2006.
Mourinho is taking nothing for granted, although he recognises wins in the remaining home games with Crystal Palace (May 3), Liverpool (May 10) and Sunderland (May 24) would be enough to seal the trophy.
"We need eight points to be champions," Mourinho said.
"Football is not about 'if', it's not about 'almost'. It's about mathematics.
"When mathematically it's done, it's done, we celebrate. Until that moment, no.
"We need two victories and two draws to be champions.
"What we can say is that we play (for) nine points at home. We can be champions just at home with the matches we play at home. "Obviously if we can get points away, it's better."
Mourinho downplayed the significance of the triumph over third-placed United, who are now 11 points behind and out of the title reckoning, despite exuberant celebrations from his players.
"Three more points," Mourinho said. "Before the game we needed 11. In this moment we need eight.
"Every point we get now, every victory we get, is one step in the title direction, but no more than that.
"If the celebration is because we beat one of the biggest clubs in the world I understand that.
"If the celebration is because the players gave everything to win that game and they feel the result of the work they did all week to prepare for this game, I understand that.
"If they are celebrating something more than that, not at all.
"I am too old on this. And I think I will be ready to work again next week and to make the players feel that there is still a long way to go."
Mourinho was reluctant to single out individuals for praise, assessing each of his players - collectively "magnificent" in performing as Chelsea had prepared - in turn.
Match-winner Hazard's appraisal was fulsome, though.
"Eden had that magic that the top ones have, especially in big matches," Mourinho added.
Mourinho was relieved Gary Cahill's trip on Ander Herrera was not punished.
Herrera was booked for diving in stoppage-time, when referee Mike Dean could easily have awarded a penalty and United the chance to equalise.
Mourinho, who has railed at a perceived "clear campaign" against Chelsea this season, added: "I am happy that it was not a Chelsea player.
"If it was a Chelsea player in this moment on Sky it would be somebody's 'crimes', would be cheating, would be the champions of the team without fair play and these kind of things.
"Because it's a Man United player tomorrow nobody remembers. So I'm happy with that."
Van Gaal refused to condemn the decision not to award a penalty, but did take issue with Hazard's goal.
The Dutchman felt Radamel Falcao was fouled by John Terry in the build up.
"You are dependent on the referee," Van Gaal said.
"When he whistles it's a penalty, now it is not a penalty.
"When he doesn't whistle for a foul on Falcao, it's not a foul.
"But my opinion is different. Okay, it's like that. I cannot control the referee."
Van Gaal expects Chelsea to wrap up the title now, but did not concede defeat.
"It is more logical that they win than we win," he added.
"It, for me, is not a surprise, but the possibility that they win the championship is much bigger now because the pressure is off for them.
"Van Gaal took some consolation in the performance of his side, but knows it counted for little.
He said: "It's amazing how we have played here. When you see the statistics it's unbelievable that the result is 1-0.
"But that's football. It's not like another sport. That counts.
"It is not that we have made a big step in our process that counts.
"For me it counts. But for the fans we have lost and Manchester United have lost. That's a pity when you play so well.
"Now I have very disappointed players and I am very disappointed. But I see that we are improving every week.
"When you can play in Chelsea like this, as the dominant team, then I'm very happy with that, but I'm very disappointed. That's the ambivalence in my feelings."