On his return to the starting XI, Hazard fired the Blues level with an angled strike after Dwight Gayle's poked effort had given the Magpies a surprise lead.
Striker Alvaro Morata made it 2-1 to the hosts when he headed in from close range following Victor Moses' driven cross.
Hazard made sure of Chelsea's 10th league win of the season with a penalty after Matt Ritchie fouled Moses in the area.
If Chelsea want to make it a three-team title race, keeping Hazard in peak condition could be key.
Nine shots, six on target, and two goals underlined why, of all manager Antonio Conte's riches, it is the former Premier League Player of the Year he cannot do without.
It was Hazard who brought Chelsea level after they were handed an early jolt by Newcastle.
Cesar Azpilicueta's ball from the right was blocked by Florian Lejeune but the loose ball found its way to the Belgium international, who smashed in his seventh goal in 10 games.
The home side then took control and led 12 minutes before half-time when Moses, who like Hazard was brought back into the line-up, bulleted a cross in the direction of Morata. The Spain international nodded in from barely a yard out.
Newcastle, perhaps fearful of a capitulation similar to the one they had at Old Trafford recently, sat back after the break.
However, Chelsea still found gaps and won a penalty when Ritchie brought down Moses. The unflappable Hazard dinked the resulting spot-kick past Karl Darlow.
The Magpies keeper then denied the Belgian a hat-trick when he stuck out a hand to claw away a shot.
Hazard was substituted to a standing ovation moments later. It was the least he deserved.