* Bayern 13 points clear at the top of the Bundesliga
* Lewandowski, Mkhitaryan grab doubles in Dortmund rout (Adds Hertha win, corrects dateline)
BERLIN, Feb 8 (Reuters) - Runaway leaders Bayern Munich survived a torrid opening against Nuremberg, who hit the bar and had two players carried off in the first half-hour, before hitting back for a 2-0 win in the Bundesliga on Saturday.
Mario Mandzukic and captain Philipp Lahm, with his first goal in more than three years, scored to give Bayern their 12th successive league win, leaving them 13 points clear at the top.
Henrikh Mkhitaryan and Robert Lewandowksi scored twice each as third-placed Borussia Dortmund thrashed hapless Werder Bremen 5-1 away, pushing the four-times champions closer to the relegation zone.
Hamburg SV's miserable run continued when the Bundesliga's only ever-present side conceded three first-half goals on the way to a 3-0 home defeat against Hertha Berlin, keeping them in the relegation zone.
Colombian forward Adrian Ramos missed a penalty but also scored two goals as Hertha handed Hamburg their sixth defeat in a row.
Champions Bayern, who have dropped only four points all season and are unbeaten in their last 45 league games, have 56 points from 20 games with second-placed Bayer Leverkusen on 43 after their 1-0 win at Borussia Moenchengladbach on Friday.
Dortmund are a further four points back while Schalke 04, fourth with 34, host Hanover 96 on Sunday (1630 GMT).
Third from bottom Nuremberg have come to life since the winter break and made a lively start as Hiroshi Kiyotake clipped the crossbar with a spectacular, acrobatic volley in the fourth minute.
Bayern then had a double let-off as Josip Drmic broke clear and was denied by goalkeeper Manuel Neuer before Jerome Boateng blocked Daniel Ginczek's follow-up from the rebound.
Predictably, Nuremberg were made to pay for their profligacy and Bayern went ahead with their first attack when Mandzukic got in front of his marker to cleverly hook in David Alaba's cross in the 18th minute for his 12th league goal of the season.
Nuremberg, who already had Timothy Chandler carried off with an injury, then lost Ginczek with an apparent knee problem and it was clear their chance had gone.
They had an extraordinary let-off when an Arjen Robben free kick hit the inside of the post and Thomas Mueller headed against the crossbar from the rebound.
Sure enough Bayern secured the points soon after halftime when Mandzukic was set free down the right and clipped the ball across for Lahm to score with a scruffy finish, his first goal since December 2010.
The league's second top scorer Lewandowski, whose double took his tally to 13, set Dortmund on the way when he struck with a sublime right-foot finish from just inside the penalty area after being set up by Marcel Schmelzer in the 26th minute.
Mkhitaryan skipped two tackles before scoring with a low shot from outside the area to make it 2-0 before halftime.
Defender Manuel Friedrich tapped in his first Dortmund goal after the break and Mkhitaryan and Lewandowski completed the rout as Dortmund ran amok against a ragged Werder defence.
Levent Aycicek grabbed a late consolation for the hosts who are 13th with 20 points, too close to the drop zone for comfort. Nuremberg occupy the relegation playoff spot with 17 points.
Hamburg stayed one point below them in 17th after a series of defensive blunders left them in disarray against Hertha.
They had a let-off when goalkeeper Rene Adler brilliantly saved a Ramos penalty in the 15th minute, only for the Colombian to outjump the defence from the resulting corner to produce a goalbound header that was turned in by Sami Allagui.
Ramos was again too powerful when he nodded the second eight minutes later. He then showed his ability with his feet as he slotted home a third on the counter attack seven minutes before the break.
First-half goals from Eintracht Frankfurt's Johaness Flum, Alexander Meier and Stefan Aigner earned a 3-0 win over bottom club Eintracht Braunschweig, lifting them to 12th.
Sixth-placed VfL Wolfsburg scored all their goals in the second half as they beat Mainz 05 by the same score. (Reporting by Brian Homewood; Editing by Ken Ferris)