Hazard was the difference between the sides, setting up the opening goal and then scoring twice in an end-to-end encounter at the Stadium of Light which helped the second-placed Blues maintain the pressure on leaders Arsenal.
Asked how he rated Hazard's individual display, Mourinho said: "The best. With me, the best.
"Maybe last season, he did something similar or even better, but with me, the best.
"The talent, we know, but the ambition from the first to the last minutes for me, it was the first time because he has a great talent, but sometimes he does incredible things and after that, he disappears from the game.
"Today, he was fantastic from the first minute, getting the ball, taking on defenders, shooting. Sometimes he creates a lot, but doesn't shoot; today the performance was fantastic.
"He, [Juan] Mata and Willian, all of them, they were creative, they were dynamic, they gave to the team what we need in terms of creation in the last phase of the game."
It was Hazard who provided the 17th-minute cross from which Frank Lampard cancelled out Jozy Altidore's opener, and he then produced two sublime pieces of skill to get his own name on to the scoresheet twice, after 37 and 62 minutes.
John O'Shea had levelled in between Hazard's efforts, and it was fellow Black Cats defender Phil Bardsley who had the final say at both ends with an 84th-minute own goal and then Sunderland's third seconds later.
Mourinho was delighted with the way his side played going forward, but disappointed with some of the defending with all the Black Cats' goals coming from set-pieces.
He said: "We played a phenomenal game, the best game away from home. It was top quality, building up well, great creativity with the three attacking players behind Fernando [Torres] - Mata, Willian and Eden - beautiful goals. Even the fourth was a nice counter-attack situation.
"The game is about that, but it is also about basic things and we failed in the basic things of the game. The most basic thing is to defend set-pieces.
"It was a very good performance. Even defensively, I think we did well, but the set-pieces... In the last six minutes of extra time, if they had two more corners, they would have won 5-4.
"When you play so well, you have to win comfortably and not give a headache to the manager in the last six minutes."
Sunderland boss Gus Poyet, a former Chelsea player, was proud of his team and remains confident they can get themselves out of trouble - they remain bottom of the table - if they perform in similar fashion for the rest of the season.
Poyet said: "If we can play like today and fight like today and make it so difficult like today, we will stay in the Premier League for sure.
"Maybe we needed one more corner today, one extra corner in the last six minutes. But we didn't get it."
The Uruguayan was as impressed as Mourinho with Hazard's contribution, admitting: "He was unplayable, Hazard, today.
"I don't remember a player performing at this level against me as a manager. He was spectacular.
"We tried everything - doubled up, tripled up, we changed the player who was playing wide. We nearly put on another full-back, but we were losing, so we couldn't.
"It was a great display, probably the best I have seen this season from an individual player."