It was a professional display from Jose Mourinho’s side, as they weathered some good attacking spells from a lively Schalke but picked their opponents off with three expertly taken goals, two via slick breakaways.
Mourinho’s side are now top of Group E after Basel could only draw with Steaua Bucharest in Romania.
Schalke’s defence was exposed early on when Frank Lampard’s inswinging corner was glanced on by Branislav Ivanovic.
The ball evaded the Schalke defence and goalkeeper Timo Hildebrand for Torres to nod in at the far post.
Schalke enjoyed plenty of possession and were dynamic in attack. Kevin-Prince Boateng, once of Tottenham and Portsmouth, Christian Clemens, Julian Draxler and Max Meyer operated as a fluid front four, without finding a clinical final pass or shot.
Twice Petr Cech saved when a Schalke player was offside, while Atsuto Uchida passed up a glorious opportunity when played in by Roman Neustadter, lifting his shot high.
Chelsea were struggling to get the ball, let alone keep it. But there were still warning signs for Schalke and a dazzling Hazard run went unrewarded as the ball became caught under the Belgian’s feet inside the box.
A Schalke surge closed the first half, with Cesar Azpilicueta blocking from Meyer when Cech could only claw away a Dennis Aogo cross before the goalkeeper tipped over a Boateng shot.
From the resulting corner Cech had to acrobatically tip over a header from the unmarked Neustadter.
The next set-piece resulted in a goalmouth scramble which ended when Benedikt Howedes backheeled wide.
John Terry then blocked from Draxler as the half ended with Chelsea’s slender advantage intact.
The visitors had little respite early in the second half, but came close to extending their advantage when Lampard lofted a free-kick into the box and Torres leapt to meet it, his header rebounding down off the woodwork.
A Schalke set-piece troubled the visitors once more when Howedes lost his marker, but headed wide.
The hosts were made to pay in thrilling style by a Hazard-inspired break.
As another Schalke attack broke down, the Belgian nipped in ahead of a sliding Aogo and burst into the Schalke half – where Oscar assumed possession.
Three blue-shirted attackers swarmed forward and the Brazilian showed great strength to hold off Jones and play the ball square for Torres.
The Spaniard’s first touch wrong-footed Hildebrand and he was able to fire in to complete a scintillating counter-attack.
Recognising Chelsea had exerted the near knockout blow, Mourinho brought on defensive midfielder John Obi Mikel for Andre Schurrle and David Luiz for Oscar.
The Blues then showed a ruthless streak with a late third. Ramires prodded the ball forward for Hazard to run half of the field, Torres provided a distraction and the Belgian tucked in to complete victory.