The 23-year-old has been in fine form of late and found the net for the London club with his ninth Premier League goal of the season, already matching his total tally from last term.
Fernando Torres added a second late on but Mourinho chose to aim the majority of his acclaim in Hazard's direction.
"He's been playing very well for a long time," the Chelsea boss told reporters. "The club made a big investment in him last year.
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"Without losing his fantastic ability and talent, he is giving us other things, so the kid is in a very good moment of his career.
"Let's see if the Premier League decides to give him Player of the Month, because maybe they don't like to go to Cobham [Chelsea's training ground]. The kid is waiting and the trophy is not arriving."
With the midfielder also being linked with a move away from Stamford Bridge - with Paris Saint-Germain being touted as a possible destination - Mourinho also played down any prospect of him leaving, adding: "He knows that Chelsea is a fantastic club for him."
Goalkeeper Petr Cech broke the club's clean-sheet record with another his 209th for the Blues and his manager was also quick to laud the long-serving Czech.
"He is almost 10 years playing at the top, since 2004 - clean sheet after clean sheet," Mourinho continued. "In this moment he beats the record of Mr [Peter] Bonetti and, I think, probably next year he will beat the record of the Premier League."
On the more general subject of Saturday's match, the Portuguese was pleased with his side's patient approach.
"In the first half, they controlled us very, very well," he added. "They defended well, they changed their system to adapt to us and they pressed.
"We didn't get frustrated, so we never lost the balance. Tactically, we always kept that shape. In the second half, when we had a bit more of the ball, we intensified the game."