David Moyes' United, after their worst start to a domestic campaign in 24 years, were held to a dour 1-1 draw by Shakhtar Donetsk in a game that went ahead without injured Wayne Rooney.
The stalemate, after Danny Welbeck's early opener was cancelled out by Taison 14 minutes from time, left United level pegging with Shakhtar at the top of Group A, after Bayer Leverkusen beat Real Sociedad 2-1.
"That was a good point coming here and getting one isn't easy," said Moyes, who was handed the unenviable job of replacing the legendary Alex Ferguson when he stepped down at the end of last season.
"Shakhtar have a great record here so to get a point is no mean achievement," the former everton boss added.
United's veteran Welsh international Ryan Giggs came on in the second half to overtake Raul with at 145 the most appearances in Europe's top club competition.
Back in Manchester, at the Etihad stadium, City were humbled 3-1 by brilliant Bayern, playing in England for the first time since claiming the trophy at Wembley last season, in a clash that reunited City's manager Manuel Pellegrini with Pep Guardiola.
The pair are old foes from Spain, when they occupied the dugouts at Real Madrid and Barcelona respectively in 2009-10.
Guardiola it was who came away with the bragging rights this time after goals from Franck Ribery, Thomas Mueller and Arjen Rbben - Alvaro Negredo getting a late consolation for City - pushed the German giants onto six points and firmly in command of Group D.
"We've got six points and we've taken a good step towards qualifying for the next stage. I think we dominated the game and we dominated possession," said Guardiola.
For City defender Micah Richards "it felt like they had an extra man" while Pellegrini conceded: "I think we played really bad.
"It's not the team we see every Sunday here in the Premier League and that was I think the worst thing."
City lie second on three points with CSKA Moscow, 3-2 winners over Viktoria Plzen, in third on goal difference.
Pellegrini's predecessor at City, Roberto Mancini, enjoyed a baptism of fire in his first game just 48 hours after being appointed coach of Galatasaray.
Didier Drogba gave Mancini the perfect start, putting the Italian's new Turkish club into the lead - but Juventus hit back with a late double from Arturo Vidal's penalty and Fabio Quagliarella before substitute Umut Bulut's bagged the equaliser two minutes from time.
"There wasn't a lot of time for me and so we went out with the idea of not giving them too much space," said Mancini.
His opposite number, Antonio Conte, reflected: "Of the two goals, the one that hurts most was the late equaliser. To concede a goal in the 87th minute always hurts, but that's football."
Galatasaray, who are bottom of Group B, had been hammered 6-1 by table toppers Real Madrid last time out and Real were at it again, drubbing FC Copenhagen 4-0 at the Bernabeu with doubles from Cristiano Ronaldo and Angel di Maria.
"We played a great match, we changed the system a bit and played with three up front," Di Maria told Spanish TV station Canal Plus.
The nine-time European kings - without Gareth Bale (thigh strain) - are well on course for the last 16, four points ahead of Juve with the Italians next up to visit Real's stronghold.
At the Parc des Princes PSG were sitting pretty on six points and occupying the Group C summit after their 3-0 win over Benfica.
The moneyed Parisians indicated they are genuine title contenders with a stunning first-half display thanks to superbly-worked goals scored by Zlatan Ibrahimovic and Marquinhos and another effort by the Swede.
"They (PSG) showed the power of their financial investment," said Benfica coach Jorge Jesus. "Last season they were knocked out by Barcelona without losing and they will compete to win the tournament this season."