On a night when all the big clubs won, defending champion Bayern Munich set a new Champions League record by winning its 10th successive game in the competition with a 3-1 win at CSKA Moscow. It equaled Barcelona's 2002-03 record with nine in a row three weeks ago.
Bayern, the only team left in the tournament with a 100 percent record, overcame freezing temperatures to come out on top of an entertaining match. Bayern leads Group D with 15 points, three more than Manchester City after the Blues won 4-2 against last-place Viktoria Plzen. Bayern and City, who had already qualified, will be vying for the group supremacy in two weeks in Germany.
Despite Cristiano Ronaldo's absence and Sergio Ramos's sending off after just 26 minutes, Madrid played superbly in the second half, scoring three goals to add to Bale's opener.
Ramos was sent off for a foul on Umut Bulut, but Madrid looked unfazed as Bale opened the scoring with an exquisite free kick from 30 meters in the 37th minute.
Bulut equalized right away but the Turkish club wilted in the second half at the Santiago Bernabeu Stadium as Madrid joined fellow Spanish teams Barcelona and Atletico Madrid in the round of 16. Chelsea also advanced on Tuesday night despite losing 1-0 against Basel.
"The second half was very good. The coach made all the right changes. Many people say that we depend on players like Xabi Alonso or Cristiano Ronaldo but we showed we can win because of the way others play," said Arbeloa.
United played its most accomplished match of the season against a poor Leverkusen team to claim its biggest away success since the Champions League format was introduced in 1992-93.
Playing without star striker Robin Van Persie and defender Nemanja Vidic, United had been expected to struggle against the German team. Instead, they cruised.
"That was a really tough evening for us," Leverkusen midfielder Simon Rolfes said. "The second goal broke down our morale a bit although we actually had a decent start to the game. After the third goal, the game was over."
Antonio Valencia put United ahead in the 22nd minute, Emir Spahic's own goal in the 30th doubled United's lead and Jonny Evans got the third in the 65th. Chris Smalling steered home the fourth in the 77th and Nani completed the rout in the 88th.
United has 11 points before its final match against second-place Shakhtar Donetsk, which beat Real Sociedad 4-0 to move onto eight points. Leverkusen has seven points while Real Sociedad has one point and is eliminated.
It was a good evening for the Manchester clubs as Alvaro Negredo and Edin Dzeko scored in the final 12 minutes to earn City a 4-2 victory over Plzen, keeping alive the English team's slim hopes of finishing top of Group D.
In Moscow, Arjen Roben fired Bayern in front midway through the first-half before Mario Gotze made it 2-0 with a solo effort early in the second half. Keisuke Honda was a constant threat after the interval and converted a penalty in the 61st minute as CSKA pulled one back. But Thomas Muller also scored from the spot to restore a two-goal lead for Bayern four minutes later.
Vidal broke the deadlock for Juventus in the 28th minute from the penalty spot after Lars Jacobsen had handled in the area. Former Juventus defender Olof Mellberg swiftly went from hero to villain for Copenhagen when he equalized in the 56th before giving away a penalty four minutes later by bringing down Fernando Llorente. Vidal again converted and headed home two minutes later to complete his hat trick.
At the Parc des Princes, Edinson Cavani scored in the final minute as 10-man PSG beat Olympiakos 2-1 to reach the knockout stages of the Champions League as group winners.
With PSG a man down for most of the second half after midfielder Marco Verratti's sending off, Olympiakos looked to have done enough to seal a valuable draw when center half Kostas Manolas equalized from close range in the 80th minute following a corner.
But Cavani ran onto substitute Adrien Rabiot's pass and finished with a powerful shot that gave goalkeeper Roberto Jimenez no chance. Verratti's sending off in the 46th handed the visitors a way back into a contest that looked easily within PSG's reach when Zlatan Ibrahimovic scored in the seventh minute on his 100th appearance in the competition.
