Schweinsteiger, whose spot-kick miss in the Munich final shootout paved the way for Chelsea to be crowned European champions, fired Bayern ahead with a deflected shot in the 38th minute, much to the delight of the 68,000 sold-out crowd in Munich.
"We were good tonight but that 1-0 was too dangerous and fragile. After we scored again we became more confident," German international Schweinsteiger told reporters.
Midfielder Toni Kroos added a second when he scored with a 20-metre drive in the 76th minute but the German side were far from convincing in their opening game.
Defensive-minded Valencia, in their first encounter with Bayern since losing to them in the 2001 Champions League final, cut the deficit with a header from Nelson Valdez in stoppage time after he beat two defenders in the air.
Bayern should then have made it 3-1 but substitute Mario Mandzukic's penalty was saved by keeper Diego Alves after Adil Rami was sent off.
In the other group game BATE Borisov stunned hosts Lille 3-1.
"We kicked off with a victory and that is what is important," Bayern coach Jupp Heynckes told reporters. "It was a game of patience for at least 30 minutes. We knew Valencia are good on the break but after the lead we got more confident."
"In the end, however, I did not like the fact that we were too relaxed and not concentrated enough. We let in that goal and then we failed to convert a penalty. We still have room for improvement," said Heynckes.
Heynckes sprang a surprise with his starting lineup, leaving top scorer Mandzukic on the bench and bringing in the experienced Claudio Pizarro. He also gave 40-million euro-signing Javi Martinez his first competitive start.
The hosts enjoyed the majority of possession but were made to work hard as cautious Valencia defended deeply. Kroos tried his luck from 20 metres but Alves was well-placed to save.
Bayern, who are top in the Bundesliga, kept at it and Schweinsteiger broke the deadlock after a well-timed pass by Arjen Robben.
"Schweinsteiger was good today and I think he did a lot. He steered our game for much of the time and showed his class," said Heynckes.
Valencia, with only one win in four league games in Spain so far, posed no real threat and waited for a chance to break, mainly relying on Algerian Sofiane Feghouli's speed for any offensive spark.
Kroos forced another good Alves save on the hour before finally beating the Brazilian after being left unmarked outside the box.
Valencia were given a ray of hope when substitute Valdez caught a sleepy defence napping and the former Bundesliga player easily headed past keeper Manuel Neuer.
Bayern then had the chance to add another but Mandzukic completed a hat-trick of penalty misses for German teams in the competition after both Borussia Dortmund and Schalke 04 missed in their games on Tuesday.
"Maybe we did have a bit too much respect," Valencia coach Mauricio Pellegrino told reporters. "That is one of the reasons fo
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