The last time Chelsea ventured on to German soil they had clinched their first European Cup. If they had been waiting since then to re-establish credentials at this elite level, last season's toils in the group section having damaged their reputation, then this resounding victory in the Ruhr valley will serve as a statement of renewed intent.

Schalke were well beaten here, wounded by neatly taken goals from Fernando Torres, a striker revived as he revels under new management, and denied the last vestiges of hope by a late third from Eden Hazard. Chelsea cut the locals to pieces every time they sprang at them at pace and José Mourinho took as much satisfaction in keeping the first clean sheet by a visiting side here in this competition in 11 matches.

There was strength as well as bite to a display that has thrust the Londoners to the top of the group.

The manager has been scarred by each of his previous matches away to German opposition, six trips to the country with three different clubs having ended in defeat. This was an emphatic way to break that duck. "I know about that [record] but I also knew that, if anyone asked me, they'd only talk about half the story," said the Portuguese. "That record is just about defeats in Germany but I've never lost at home against a German team either. But this game was good for us. We controlled the match and were dangerous. We deserved the points."

It was the revival of Torres that truly caught the eye. This was the Spaniard's 100th start for this club and his tireless industry was rewarded with a double to take his Chelsea tally to 38. He might have celebrated a hat-trick had a thumped header early in the second half not cannoned down from the angle of the post and bar with Timo Hildebrand helpless, although that mattered little.

A player who has managed only a solitary Premier League goal this calendar year still finds Europe to his liking, his improvement under Mourinho clearly not overly affected by the untimely knee injury suffered at Steaua Bucharest three weeks ago.

His goals here were pilfered cannily. The visitors had already threatened twice in the opening five minutes when charging from deep – Oscar, Hazard and André Schürrle gliding at pace against back-tracking opponents – when Schalke ignored Torres's presence at the far post from Frank Lampard's corner. The delivery was flicked on by Branislav Ivanovic to confound the German back line and the striker duly nodded into the unguarded net from close range.

There was a vulnerability to the home side throughout, a reflection of the 19 goals shipped in nine Bundesliga matches this term and recent injuries that have disrupted them.

Chelsea might have added a second long before their rivals surrendered possession sloppily, not for the first time, in central midfield, allowing the visitors to break at pace. Oscar held off Jermaine Jones, who eventually pulled up in the duel, and slid the ball inside for Torres to collect. The 29-year-old took his time to wrong-foot the goalkeeper before guiding in his second and, even with 21 minutes remaining, the contest seemed settled. Hazard's third, the Belgian having waltzed with Torres into the German half with only a panicked Joël Matip to thwart them, was his first for the club in this competition and fine reward for his own excellence. Chelsea have registered 14 times in four matches, their form having clicked since half-time at White Hart Lane late last month. That seems an age ago.

"We can still improve, though," said Torres. "The first half was tight but in the second the individual quality made the difference. As a team we are feeling much better. Individually, too. I've felt sharp and well in the last few games but we have three very good strikers and we all need to be ready, every one of us. The competition is healthy." Samuel Eto'o and Demba Ba have also impressed on occasion in recent weeks. There are suddenly options for Mourinho in a position that, not long ago, looked to be this team's achilles heel.

Yet just as satisfying for the management was the ability to blunt Schalke, even with the Germans weakened by injury. They had recovered their poise from the early concession to threaten in the period up to the interval, only for Petr Cech to save well from Kevin-Prince Boateng and Roman Neustädter and his back line to suffocate almost everything flung at them.

César Azpilicueta, employed at left-back in preference to Ryan Bertrand and in the absence of Ashley Cole, blocked smartly from Max Meyer and Julian Draxler. John Terry and Gary Cahill were committed and imposing, Ramires and Lampard busy as a further shield. This was a collective show of strength. Life looks rosier from the top of Group E.