Rosenborg, who stunned the European football fraternity with a 1-1 draw at Chelsea on matchday one, had no answer to in-form Schalke, who have put together an unbeaten run in the Bundesliga this season.

Second-half strikes from Jermaine Jones and Kevin Kuranyi proved the difference between the two sides, although in truth the margin of Schalke’s victory could have been much greater against a Rosenborg side looking short of ideas in attack.

The German visitors made a bright start and there were just 40 seconds on the clock when Zlatan Bajramovic fired in a shot from the edge of the box that was blocked by Miika Koppinen.

Three minutes later Kuranyi had a decent effort from just inside the area while Bajramovic came close again as Schalke looked determined to transfer their fine domestic form into Europe.

On 25 minutes Koppinen was again on hand to block Jones’s shot for Schalke, while on 28 minutes Steffen Iversen, recalled to the Champions League starting line-up after his hat-trick in the 4-3 Tippeligaen defeat to Fredrikstad FK at the weekend, carved out the hosts’ first chance of the evening.

The former Tottenham striker took aim from 18 yards but Schalke goalkeeper Manuel Neuer had it covered and gathered with ease.

Kuranyi had another sighter for the visitors on 35 minutes but was unable to force home goalkeeper Lars Hirschfeld into a meaningful contribution.

Alexander Tettey forced Jones into a block on a rare foray into the Schalke area a minute before half-time, and there was still time for Jones to go up the other end and bring a save from Hirschfeld with a long-range drive.

Schalke began the second period as they started the first, throwing caution to the wind against their Norwegian opponents as Benedikt Howedes fired in a sighter from 18 yards that flew over Hirschfeld’s bar.

Iversen snuck in with a header on 50 minutes that flew just wide of Schalke goal, but the host were struggling to get into the game and Schalke soon went ahead.

Jones was the goalscorer on 62 minutes, firing home from just inside the box with a left-footed effort.

Rosenborg sought to raise their game after falling behind, and almost drew level on 72 minutes when Koppinen’s header from Marek Sapara’s corner was punched to safety by Neuer.

To their credit, Rosenborg kept pushing right to the death, and could have replicated their result against Chelsea had Didier Konan been able to get his shot on target with five minutes to go.

As it was, Schalke finished the game off with just two minutes remaining, Kuranyi finally rewarded for a tireless performance with a right-footed shot from the edge of the area that nestled in the back of the net.