The Blues had an opportunity to climb to the summit with Arsenal and Manchester City not in action on Saturday, and made the vital breakthrough on 56 minutes when Hazard cut inside from the left and drilled a powerful finish into the bottom corner.
Hull had carved out some good chances in a bright first half for the home side, but after Hazard’s goal they rarely threatened an equaliser and it was a relatively comfortable afternoon for Petr Cech as he kept the 209th clean sheet of his Chelsea career to break Peter Bonetti’s club record.
Torres then put the result beyond any doubt with a classy late run and shot to take Chelsea one point clear of the Gunners.
Hull had settled the quickest at the start, with Tom Huddlestone showing a calmness on the ball that relaxed the hosts.
It was Steve Bruce’s men who had the first shot of the game in the seventh minute, but Ahmed Elmohamady’s effort was never likely to trouble Cech.
The Egyptian saw plenty of the early action, three times beating Ashley Cole for pace without ever finding a cross to match.
Chelsea’s first real chance saw Torres spring the offside trap but by the time he had set himself to shoot Alex Bruce was back to make the block.
By and large, though, it was Hull doing the best work. Jake Livermore had one decent effort from distance – denied by Cech after Yannick Sagbo had gamely held the ball up in the corner under close attention from Gary Cahill.
But it was Sagbo himself who had the Tigers’ best chance. John Terry was the culprit, sending a reckless pass across his own area only for Livermore to partially intercept and send the ball spinning towards Sagbo.
The Ivorian shot first time from 10 yards but missed the target and spared the Chelsea captain’s blushes.
The visitors were stronger after that and were only denied a goal of their own by a remarkable Allan McGregor save.
Ramires’ deft chip gave Hazard room to place his cross from the byline and when it reached Oscar close to the penalty spot, the Brazilian seemed certain to convert.
In truth he did little wrong, shooting powerfully towards the roof of the net, but McGregor reacted superbly to divert the ball over the crossbar.
The Scotland keeper was required again just before the break when David Luiz’s swerving free-kick threatened to creep under the crossbar and the half-time whistle came as a welcome break for the hosts.
Hazard emerged as the man most likely to get Chelsea on the scoresheet as the second period began, beating two men on his way into the area and winning a corner before helping earn a dangerous free-kick.
Luiz aimed for the near side of goal but again found McGregor alert to the danger.
Hazard eventually took the responsibility himself. Luiz and Cole played him in after a neat combination on the left and the Belgian produced what is fast becoming his trademark finish.
He cut inside twice to create his preferred angle, wrongfooting the Hull defence and leaving Bruce sprawling, before clinically finding the bottom corner.
The game was not without entertainment in the final half hour, but there was an unavoidable sense that Hazard’s effort had settled things.
A Huddlestone free-kick was Hull’s likeliest chance but came to nothing, while Chelsea had plenty of possession in the final third and should have made life easier on themselves.
Willian, in particular, sparked into life and began picking holes in the Tigers defence.
Oscar was denied a near-certain goal for the second time in the match when Curtis Davies deflected his close-range effort over but Torres did make sure in the 87th minute.
He had enough pace to jockey Bruce out of position as he bore down on goal and finished crisply to secure the points.