The European champions, who were humbled 3-0 by tiny Eibar last week, took a fortuitous lead when Valencia midfielder Daniel Wass nodded a Dani Carvajal cross into his own net in the eighth minute after former Arsenal defender Gabriel Paulista had failed to clear the danger.
Third-placed Inter Milan scored twice in the last six minutes through Stefan De Vrij and Alessandro Bastoni to snatch a 2-1 win at Parma in Serie A on Sunday despite a subdued display. The scarcely-deserved victory left Inter eight points behind leaders Juventus and four adrift of second-placed Lazio with 10 games each to play.
Second half goals from Presnel Kimpembe and Kylian Mbappe gave the impressive French side a clear advantage ahead of the return in Paris on March 6.
The Spaniard missed the 2-1 defeat after injuring his hamstring against Manchester City before the international break.
Norway defender John Arne Riise completed his move from AS Roma to Fulham on Wednesday, saying he was delighted to be back in the Premier League and looking forward to joining his brother Bjorn Helge at Craven Cottage.
AS Roma midfielder Daniele de Rossi received a three-match ban on Friday for an off-the-ball incident in last week's Champions League match against Shakhtar Donetsk.
The victory moved second-placed Bayern, who take on Celtic in the Champions League next week, up to 17 points, two behind Dortmund who suffered their first home loss in 41 league matches.
Seydou Keita cancelled out a superb Carlos Tevez free kick as second-placed AS Roma fought back with 10 men for a fiery 1-1 draw at home to leaders Juventus who stayed on course for a fourth successive Serie A title on Monday.
AS Roma midfielders Daniele De Rossi and Simone Perrotta will miss their side's late push for a Champions League qualifying spot after Serie A confirmed their three-game bans in a statement on Tuesday.
A late Simone Pepe goal earned Juventus a 1-0 win at Lazio on Monday to keep alive their hopes of qualifying for Europe.
AS Roma kept alive their faint hopes of landing a Champions League spot next season with an eye-catching 1-0 victory over Chievo Verona at the Stadio Olimpico on Saturday.
"I don't know how this affects my future," Valverde said.
Serie A champions Juventus became on Monday the latest team to be sanctioned for anti-Naples chanting by their fans during a game, the Serie A league said in a statement.
Internacional forward Paolo Guerrero missed a late penalty and then had a goal disallowed as his side were held 1-1 by Athletico Paranaense in Brazil's Serie A on Thursday.
News of all that's transpired on and off the football field
Barcelona and Shakhtar Donetsk became the first teams to reach the Champions League quarter-finals with contrasting wins over Arsenal and AS Roma, who both finished with 10 men, on Tuesday.
AS Roma needed a last-minute penalty from David Pizarro to win 2-1 at lowly Lecce in Serie A on Friday and boost their confidence ahead of Tuesday's Champions League clash with Shakhtar Donetsk.
Liverpool will feel the weight of increased expectation to deliver silverware this season after making encouraging forays into the transfer market, manager Juergen Klopp said.
Substitute Alexandre Pato netted a superb winner after Robinho had opened the scoring using the top of his arm as Serie A leaders AC Milan ground out a precious 2-1 win at Chievo on Sunday.
Barcelona suffered a 2-1 defeat at Arsenal and AS Roma's miserable run continued with a 3-2 home loss to Shakhtar Donetsk in Champions League last-16 first-round matches on Wednesday.
Antonio Cassano scored his first AC Milan goal and Robinho struck twice to help the Serie A leaders end a run of two straight draws in a 4-0 home thrashing of Parma on Saturday.
The Italian federation (FIGC) is determined to complete the season and its president Gabriele Gravina has been presenting new ideas on an almost daily basis of how that can be done. Meanwhile, Turkmenistan in Central Asia is set to resume its soccer season with spectators at the weekend, making it only the second country in the world to let fans attend matches as the new coronavirus shuts down almost all of world football.
Mirko Vucinic helped to send AS Roma into the Italian Cup semi-finals with a superb goal to set up a 2-0 win at Juventus on Thursday.
AS Roma soothed internal strife by clambering up to second in Serie A with an easy 3-0 home win over Cagliari on Saturday.
In other ties, Serie A champions Juventus face Europa League winners Atletico Madrid and Barcelona take on Olympique Lyonnais.
AS Roma captain Francesco Totti, who has been at his hometown team his whole career, hinted for the first time on Tuesday that he could leave the club after a row with coach Claudio Ranieri.
Manchester City must rebuild for title challenge: Guardiola
Juventus' wretched start to the season continued when they needed a late penalty to avoid defeat as the Serie A champions were held to a 1-1 home draw by early leaders Chievo Verona on Saturday.
News of all that's transpired on and off the football field
Serie A leaders AC Milan lost 1-0 to AS Roma after striker Marco Borriello burst his former club's bubble and put his new side back in the title picture at a freezing San Siro on Saturday.
Kevin Prince Boateng scored the first goal and impudently set up Robinho for the second to help rampant Serie A leaders AC Milan to a 3-0 win at troubled club Bologna on Sunday.
On a good night for English clubs in the Europa League, Manchester United hammered AZ Alkmaar 4-0, while Wolverhampton Wanderers also thrashed Besiktas 4-0 in Group K, and Arsenal came from two goals down to draw 2-2 away to Standard Liege and finish first in their pool. The upset of the night came in Group J as Crivelli scored a 90th-minute winner against Borussia Moenchengladbach to send Basaksehir through and knock the Germans out, with AS Roma grabbing the runner-up spot thanks to a 2-2 home draw with Wolfsberger as the Europa League group stage concluded on Thursday.
Lazio goalkeeper Fernando Muslera watched in horror as Marco Borriello's weak penalty crept under his body and dribbled into the net to help city rivals AS Roma to a 2-0 win over the Serie A leaders on Sunday.
AS Roma supporters may be looking ahead to Barcelona's Champions League visit with some trepidation and coach Rudi Garcia certainly does not seem to be bursting with optimism.
Thousands of fans and dozens of players turned out on Thursday to say goodbye to Fiorentina captain and Italy international Davide Astori, who died suddenly at the age of 31 on Sunday.
Juventus clinched a place in the Champions League knockout stages when a brilliant Cristiano Ronaldo assist set up Mario Mandzukic to give them a 1-0 win over Valencia on Tuesday.
Diego Milito put a forgettable month behind him by grabbing his first goals of the season to send champions Inter Milan clear at the top of Serie A with a 4-0 romp over Bari on Wednesday.
Last season's runners-up AS Roma were held to a scrappy 0-0 draw by promoted Cesena on Saturday in their first match of the Serie A season.
European champions Inter Milan were grouped with Werder Bremen, Tottenham Hotspur and Twente Enschede in the draw for the Group Stage of the Champions League on Thursday.
Roma have signed Norwegian international defender John Arne Riise from Liverpool for $7.74 million, the Italian Serie A club said on Wednesday. Riise has signed a four-year contract, a statement on the club's Web site said.