The drama at Bayern Munich took place off the pitch with Carlos Tevez refusing to come on for Manchester City during its 2-0 loss.
Tevez's former club United threw away a 2-0 halftime lead against Basel and the three-time champions required Ashley Young's 90th-minute header to recover a second successive draw in Group C.
Real Madrid swept aside Ajax after goals from Cristiano Ronaldo, Kaka and Karim Benzema in the Group D meeting of two sides with 13 European Cups between them.
Inter Milan picked up its first points in Group B after Mauro Zarate clinched a 3-2 win at CSKA Moscow but Trabzonspor stays top after drawing 1-1 with Lille.
At Old Trafford, United did not appear to miss its injured first-choice strike force of Wayne Rooney and Javier Hernandez.
The 20-year-old Danny Welbeck scored twice in two minutes in the first half to put United 2-0 up by the 17th minute, with 37-year-old Ryan Giggs providing both goals.
But United's defense crumbled in the second half after Fabian Frei pulled Basel's first goal back in the 58th minute.
Alexander Frei headed Basel level two minutes later after meeting Fabian Frei's cross and then put the Swiss champion in front from the penalty spot in the 76th after Antonio Valencia fouled Marco Streller.
But Young produced a late leveler, sending a downward header into the net after meeting Nani's cross.
The draw leaves United winless and with just two points after two matches, while Basel is top of the group with four along with Benfica, which beat newcomer Otelul Galati 1-0.
"We were careless.. it's a wake-up call in many ways," United manager Alex Ferguson said. "A lack of concentration saw us give the game away really ... but we rescued it."
There was no comeback in Munich for Manchester City as Mario Gomez twice knocked in rebounds from Manchester City goalkeeper Joe Hart to put Bayern 2-0 up before half time.
The victory left Bayern in control of Group A with a perfect record after two games, while City has one point as well as having to deal with insubordination.
City manager Roberto Mancini wanted to bring Tevez off the bench in the second half as City was trying to recover from 2-0 down, but the Argentina striker refused to take the field.
"If I have my way he will be out of the club," Mancini said, while stressing that the club's Abu Dhabi owners would make the final decision. Despite being the Premier League's joint top-scorer last season, the striker has featured infrequently this campaign after failing to secure a transfer away from Manchester in the offseason.
City is being kept off the bottom of Group A by Villarreal, which has no points after losing 2-0 at Napoli.
After Marek Hamsik's 14th-minute opener, Edinson Cavani doubled the lead from the penalty spot three minutes later.
Real Madrid enjoyed the biggest victory of the night to stay top of Group D and leave Ajax on one point.