Bayern played the last few minutes at Old Trafford with 10 men after Schweinsteiger, who scored their equaliser in the 67th minute, got a second booking for tripping Wayne Rooney, ruling him out of next Wednesday’s second leg at the Allianz Arena.
Schweinsteiger’s superbly taken first-time lash into the roof of David De Gea’s net came nine minutes after United skipper Nemanja Vidic stretched to clinically head a Rooney corner past stranded goalkeeper Manuel Neuer in the 58th.
“Congratulations to the team,” Bayern coach Pep Guardiola told reporters. “I am satisfied because Manchester United is one of the best teams in the world and that is something we should not forget.
“The away goal is extremely important even though the 1-1 can be tricky. We will try to win the return leg and I have full confidence in my players,” added the Spaniard whos team are still on track to repeat the treble they claimed last season.
United’s performance was in stark contrast to their recent 3-0 home defeats by arch-rivals Liverpool and Manchester City in a lacklustre Premier League campaign.
Although the draw ended United’s run of four straight Champions League home wins this season, it was a huge improvement on much of their domestic league form which has left them stranded in seventh place in the table.
Manager David Moyes, who has endured a tough baptism this season after taking over from the retired Alex Ferguson, had said his main wish was to have a foothold in the tie going into the second leg and he was encourged by United’s performance.
“I was really pleased with the way we played there was a great atmosphere a great crowd, it was really gutsy, ” he told ITV Sport.
“There was a real determination tonight to make sure we did well. It’s a competition we have a really good history in, and we played a really good side tonight.”
With Schweinsteiger and defender Javi Martinez now suspended for the return, Moyes was asked if he had more belief in winning next week against a side who retained their domestic title with seven matches left and are in the German Cup semi-finals.
“Well we have to score a goal because if the score stays as it is, Bayern goes through and we have to do something about it.
“We said we wanted to go into the second leg with a real chance and we have done that. We have given ourselves a real opportunity. We will go to Munich and try and get a victory.”
Bayern had won their last four matches on English soil in the last 13 months, including two wins at Arsenal, a victory at Manchester City and success in last season’s Champions League final when they beat Borussia Dortmund at Wembley.
After a scare when United’s Danny Welbeck saw a goal ruled out after five minutes for raising his foot too high, Bayern looked capable of extending that winning run, and taking their overall Champions League away record to eight successive wins.
They established a grip on the game, creating seven scoring chances in the opening 35 minutes, as defenders David Alaba and Rafinha poured forward to support the attack and they looked sharper to the ball than the home side.
But, for once, the German side, who had scored in their last 60 matches in all competitions, appeared to have lost their cutting edge in front of goal.
The best of those first-half efforts came after 31 minutes when winger Arjen Robben was allowed too much space and De Gea had to dive full length to beat away his inswinging shot.
Despite being overrun by Bayern’s attacking momentum, United had the best chance before the break when Rooney found fellow England striker Welbeck with a low through ball after 40 minutes which Bayern defender Jerome Boateng attempted to block but fell over instead.
That allowed Welbeck time and space to beat Neuer but his weak chip gave the keeper the chance to paw the ball safely away.
Ryan Giggs, making his 141st Champions League appearance, one short of Raul’s record, suffered a groin injury and had to be replaced by Shinji Kagawa at halftime.
The enterprising Japanese midfielder, who never lost to Bayern when he was at Dortmund, caused the visitors plenty of problems with some intelligent runs and passes.
From one of them United won a corner which Rooney swept into the box. The ball went slightly behind the incoming but unmarked Vidic who turned his head to nod past Neuer for his first goal in Europe for more than five years.
United only led for nine minutes though before Schweinsteiger replied.
Dutchman Robben came close to a late goal for Bayern but, despite only drawing, the tie is balanced in their favour before as they prepare for the return in Germany next week without Schweinsteiger and Martinez.
(Reporting by Mike Collett; editing by Ken Ferris)