Shakhtar Donetsk led the way for the Champions League underdogs as they beat holders Chelsea 2-1 while FC Nordsjaelland were close to winning for the first time in the competition before drawing 1-1 with Juventus on Tuesday.
Barcelona came from behind and needed a goal in the fourth minute of stoppage time to beat Celtic 2-1 while Manchester United trailed by two goals before rallying to overcome Braga 3-2 at Old Trafford.
Alex Teixerra put impressive Shahktar ahead after only three minutes in Donetsk before Fernandinho doubled the Ukrainian side's lead early in the second half.
Oscar grabbed a consolation for Chelsea in the 88th minute as the Londoners lost in the competition for the first time since they lifted the European Cup last May.
The victory lifted Shakhtar to the top of Group E on seven points, three above Chelsea who have four.
Juventus, who have now drawn their last nine European matches, have three points with Nordsjaelland picking up their first point in the competition.
Nordsjaelland, ahead through a 50th minute Mikkel Beckmann goal, were just nine minutes away from a memorable victory before Mirko Vucinic equalised for Juve in the 81st minute.
Manchester United did well to avoid an upset at Old Trafford, coming from behind to beat Braga 3-2 after being 2-0 down to an Alan double in 20 minutes. They fought back with two headers from Javier Hernandez either side of a Jonny Evans goal.
It was United's third successive win and they top Group H with nine points, followed by CFR Cluj on four after they drew 1-1 at Galatasaray. Braga have three and the Turkish side one.
In a lively match in Istanbul, Cluj had Matias Aguirregaray sent off after 28 minutes and Felipe Melo missed a penalty for Galatsaray seven minutes later.
Dany Nounkeu put through his own net to give Cluj the lead after 19 minutes before Burak Yilmaz equalised for the home side 13 minutes from time.
Barcelona needed a stoppage time Jordi Alba goal to win 2-1 after Celtic had taken the lead at the Nou Camp through Javier Mascherano's own goal after 18 minutes before Andres Iniesta's brilliantly-worked equaliser just before halftime.
Barca lead Group G with nine points from three wins, ahead of Celtic on four while Spartak Moscow have moved on to three points after their first win of the campaign, 2-1 at home to Benfica thanks to Jardel's own goal.
Valencia ended BATE Borisov's perfect start in Group F with Roberto Soldado's hat-trick securing a 3-0 win in Belarus. With Bayern winning 1-0 at Lille with a Thomas Mueller penalty, Valencia, BATE and Bayern all have six points with Lille on none.