* Substitute Pizarro, Thiago stage Bayern comeback
* Bavarians stretch unbeaten run to 43 league games (Updates with quotes, details)
BERLIN, Jan 29 (Reuters) - Thiago Alcantara's sensational flying volley in stoppage-time earned Bayern Munich a 2-1 win at VfB Stuttgart on Wednesday, extending their unbeaten run to 43 league games and increasing their Bundesliga lead to 13 points.
The Spaniard, who set up substitute Claudio Pizarro for the equaliser, completed what looked like an unlikely Bayern comeback, thundering in his volley in full flight seconds from the end to lift his side to 50 points.
"I want to congratulate the team because this is Bayern Munich," said a beaming Thiago, who joined from Barcelona last summer but has struggled with injuries.
"Stuttgart have a good team and they made it hard for us. I was lucky to have scored such a beautiful goal," he told reporters.
The Bavarians looked to be heading towards their first league defeat since October 2012 when Bosnia international Vedad Ibisevic pounced from what looked like an offside position to beat keeper Manuel Neuer in the 29th minute.
Last season's treble winners were clearly lacking their usual attacking drive with wingers Arjen Robben and Franck Ribery injured and holding midfielders Bastian Schweinsteiger and Javi Martinez yet to make their comebacks this year.
Bayern's top striker Mario Mandzukic, dropped from the squad last week for lack of commitment in training, was back in but left on the bench at the start of the game which was postponed in December.
Stuttgart conceded little space, pressing the Bavarians high in their own half and the hosts were rewarded with Ibisevic's 10th goal of the campaign.
"We played a really good game," said Stuttgart coach Thomas Schneider. "Bayern had more possession but we had our chances and deserved at least a point tonight."
Bayern left their comeback fight late and in a frantic last 20 minutes had Stuttgart boxed in and on the back foot.
Peru forward Pizarro, the Bundesliga's all-time foreign leading scorer, timed his header perfectly to meet a Thiago free kick in the 76th minute.
The Spaniard then turned scorer himself when he jumped high in the box to meet a Rafinha cross and volley in the winner. (Reporting by Karolos Grohmann, editing by Ed Osmond/Rex Gowar)