The Belgium international scored two superb solo efforts to guide Chelsea past a resilient Sunderland side, whose performance at the Stadium of Light belied their bottom-of-the-table position.
Jozy Altidore's first top-flight Sunderland goal had put the hosts ahead, but Frank Lampard's header and Hazard's low drive saw Chelsea lead 2-1 at half-time.
Sunderland equalised from an unlikely source in the shape of defender John O'Shea after the break, only for Hazard to once again take centre stage by beating two defenders and driving an effort inside the far post.
Chelsea then opened up a two-goal cushion as Phil Bardsley turned home Demba Ba's cross, but the Sunderland full-back notched at the right end in the closing stages to ensure a nervy finish.
Mourinho was delighted with Hazard's individual impact, as well as emphasising the role played by fellow attacking midfielders Willian and Juan Mata.
"It was by far our best performance away from home," he told Sky Sports. "We played fantastic football, we created chances, we had the ball, we were creative and dynamic.
"We had a special Hazard, but also Mata and Willian in front of our midfield players played a fantastic match.
"The performance was great, individually and collectively. I don't normally like to praise individual performances but tonight I have to because Eden was absolutely fantastic."
Despite the scoreline suggesting Chelsea had defensive frailties, Mourinho was happy with their display at the back, although he admitted it was "ridiculous" to concede three goals.
He added: "We played well defensively, we always had control of the situation. We conceded ridiculous goals.
"You play so well away from home and you score away from home, (but) you have to concentrate until the end (because) we conceded three poor goals. To concede three goals is ridiculous."
