Schalke 04 extended their six-match unbeaten run with a 2-0 win at home to Hanover on Sunday to stay fourth in the Bundesliga behind run-away leaders Bayern Munich.

Schalke host Cristiano Ronaldo's Real Madrid in the last 16, first leg of the Champions League later this month and have hit form after back-to-back defeats in December with three straight wins since the winter break.

The Royal Blues put on a regal performance at Gelsenkirchen's Veltins Arena with Jefferson Farfan tapping home after a superb run from defender Sead Kolasinac on 39 minutes.

Teenage wunderkind Max Meyer added a second a minute before the break.

"That was a very good performance we put in," enthused Schalke coach Jens Keller, who said defender Atsuto Uchida picked up a leg injury and midfielder Roman Neustadter had a badly cut knee.

The defeat ended Hanover's recent form having won their first two games of the year under new coach Tayfun Korkut to leave the guests lying tenth.

Earlier, ten-man VfB Stuttgart dropped closer to the Bundesliga's relegation battle after suffering their fifth-straight defeat in a 4-1 rout at home to buoyant Augsburg.

"There's no need to discuss the performance," fumed Stuttgart coach Thomas Schneider.

"Their victory was deserved and I am very, very disappointed, we must apologise to the fans as we gifted the three points in a ten-minute spell.

Bavarian minnows Augsburg are dreaming of international football next season as they rose to eighth after a sixth consecutive game unbeaten.

Two goals by midfielder Andre Hahn did the damage for Augsburg, who set a new club record of nine victories in a Bundesliga season at Stuttgart's Mercedes Benz Arena.

To compound the hosts' misery, Stuttgart had captain Vedad Ibisevic sent off with 53 minutes gone for striking Augsburg's Jan-Ingwer Callsen-Bracker in the face.

The defeat leaves Stuttgart 14th in the table, only two places from the relegation zone.

Hamburg are also deep in the relegation mire after they were thrashed 3-0 at home to Hertha Berlin on Saturday night to set an unwelcome club record of six straight defeats.

Colombia striker Adrian Ramos, who has been linked to Real Madrid and Borussia Dortmund for next season, scored twice to leave Hamburg second from bottom as they were booed by their own fans at the final whistle.

Several senior stars, including captain Rafael van der Vaart, found themselves pelted by missiles when they went to calm angry fans after the game.

Hamburg have said they will continue with coach Bert van Marwijk, but results must improve.

Third-placed Borussia Dortmund romped to a 5-1 win in Bremen on Saturday.

Dortmund dismantled Werder Bremen with Poland striker Robert Lewandowski and attacking midfielder Henrikh Mkhitaryan both scoring twice.

The thrashing came at a price as both Germany midfielders Marco Reus and Sven Bender are ruled out of this week's double header against Eintracht Frankfurt on Tuesday in the cup and in Saturday's league match.

This was the 12th time this season Bremen have conceded three or more goals and coach Robin Dutt is under increasing pressure with his side 13th and just three points from the relegation places.

Leaders Bayern extended both their unbeaten Bundesliga records with a 2-0 win at Nuremberg to remain 13 points clear in the Bundesliga as the runaway leaders left Nuremberg with 56 out of a possible 60 points this season.

This was Bayern's 45th unbeaten Bundesliga match, dating back to October 2012, and their 29th unbeaten away league game to extend their records with a rare win in Nuremberg.

Goals either side of half-time by striker Mario Mandzukic and captain Philipp Lahm sealed the win.

In the basement battle, Eintracht Frankfurt moved up to 12th with a 3-0 win at home to bottom side Eintracht Braunschweig.

Freiburg were held to a 1-1 draw at home to Hoffenheim while sixth-placed VfL Wolfsburg enjoyed a 3-0 win at home to Mainz 05.

On Friday, second-placed Bayer Leverkusen enjoyed a 1-0 win at Borussia Moenchengladbach with South Korea's Son Heung-Min scoring the second-half winner.