Liverpool exposed previous leader Arsenal's frailties in a 5-1 drubbing of the Gunners at Anfield and third-placed Manchester City was held to a goalless draw at Norwich.
Hazard, coming off an excellent performance in Chelsea's surprise win at City on Monday, scored twice within seven minutes in the first half and added another goal from the penalty spot after the interval as the Blues leapfrogged bitter rival Arsenal.
Liverpool went on a scoring rampage at lunchtime, netting four times in the first 20 minutes to end Arsenal's eight-match unbeaten sequence with a bang.
"It was a very poor day. We were poor defensively, offensively," Arsenal manager Arsene Wenger said after the hammering. "Liverpool played very well, so congratulations to them. But it was a poor performance on a day when we couldn't afford it."
The loss will again raise questions about Arsenal's abilities to win its first title since 2004 with the Gunners having already lost 6-3 to Manchester City earlier this season.
"Defensively we need to be more stable," Wenger said. "Today we were too open. From the front to the back we were not at the level we are used to."
City's current goal drought continued as Manuel Pellegrini's team missed the chance to move top of the standings. Saturday's draw left City third with 54 points, two behind Chelsea.
Hazard's first goal came in the 27th minute, with the Belgium playmaker slotting home from Branislav Ivanovic's pass from the right. Chelsea scored again on the counter-attack as Hazard played a beautiful one-two with Samuel Eto'o.
"I know today we are top of the league but I look to fifth place," Mourinho said, playing down the importance of his team's result. "I look to Tottenham vs Everton and Manchester United vs Fulham tomorrow and I want to be far from fifth. When we are far from fifth and have a Champions League position under control, then it will be time to look at Arsenal, Manchester City and Liverpool and see where they are and see the distances."
City had scored 68 goals from 23 league matches before losing 1-0 to Chelsea and again struggled at Carrow Road against lowly Norwich, which earned a crucial point in the relegation fight.
City hit the crossbar in the first half through a header from Alvaro Negredo but Norwich goalkeeper John Ruddy otherwise spent a quiet afternoon as the Canaries missed a chance to snatch victory in stoppage time when Nathan Redmond's cross flew through the six-yard box just ahead of Ricky van Wolfswinkel.
At Anfield, the Reds reignited their title challenge with a victory that boosted their hopes of finishing in the Top 4 as they look to secure Champions League football next season.
Liverpool was irresistible in the early stages and all over Arsenal defenders, with every attack tearing apart the Gunners. Martin Skrtel scored in the first minute and doubled his team's lead nine minutes later. Raheem Sterling then made it 3-0 before Daniel Sturridge beat Wojciech Szczesny with a left-footed shot in the bottom corner. Sterling then completed a brace after half-time.
Mikel Arteta pulled one back for Arsenal from the penalty spot.
"We went out there and did what the manager told us. The first 20 minutes were unbelievable and it's about the team. We worked as a team and we are getting results. It starts form the back and the boys have been excellent," said Sturridge in his post-match interview.
Arsenal, which was handed its first defeat at Liverpool since 2007, will be looking for revenge when the two sides meet a week on Sunday in the FA Cup fifth round at the Emirates.
In the bottom half, Crystal Palace leapfrogged West Brom and sent their opponents into the relegation zone with a 3-1 victory at Selhurst Park. Tom Ince and Joe Ledley scored on their debut for Palace, which has taken 16 points from a maximum 21 at home under manager Tony Pulis, who took over after Ian Holloway resigned last October with the Premier League club five points adrift of safety.
Thievy Bifouma pulled one back for West Brom after the interval before Marouane Chamakh sealed the game from the penalty spot.
Swansea manager Garry Monk enjoyed a perfect start as his team won the south Wales derby 3-0 against Cardiff to move away from the relegation zone and Hull moved a point above Palace after winning 2-0 at 10-man Sunderland.
West Ham moved two points clear of the relegation zone with a 2-0 win at Aston Villa and Southampton drew 2-2 with Stoke in a mid-table encounter.