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 the direction of Hazard.
"He's been playing very well for a long time," said the Chelsea boss. "The club made a big investment in him last year.
"Now the player is no longer a talented kid, he is now more than that. He is a player that feels and accepts the responsibility, feels and accepts that a team player is more than a talented player.
"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 shut-out, the 209th for Mourinho's men, 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 generaly subject of Saturday's match, Mourinho 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."