Match officials stopped play after 31 minutes, ruling the field was too dangerous to play on. The last hour will now be played on Wednesday, kicking off at 3pm local time (1300 GMT).
Olympiakos beat 8-man Anderlecht 3-1 to advance, edging out two-time champion Benfica, whose 2-1 victory over Paris St. Germain was not enough.
Leverkusen won 1-0 at Real Sociedad to finish behind Group A winner Manchester United, which beat Shakhtar Donetsk 1-0.
Cristiano Ronaldo became the first player to score nine times in group play as the Portugal forward's 26th goal of the season helped carry Real Madrid to a 2-0 victory at Copenhagen to wrap up Group B.
"We're first in the group, the team played very well on a very bad pitch," Ronaldo said. "I scored a goal and I'm happy that I can help the team."
Manchester City finally managed to secure a victory over a European heavyweight, coming from behind to win 3-2 at Bayern Munich to end the defending champion's record winning streak at 10 games.
City fell one goal shy of taking Group D over Bayern on head-to-head results after the clubs finished tied on 15 points.
Bayern charged into a 2-0 lead by the 12th minute at the Allianz Arena before David Silva began the rally with a 28th-minute goal. City was inspired by the Spain midfielder and, after Aleksandar Kolarov equalized from the penalty spot, James Milner side footed home a low screamer to secure the win in the 62nd.
"This is a very important result for us," City coach Manuel Pellegrini said.
Back in Manchester, Phil Jones scored in the 67th minute at Old Trafford as United continued to find its form in Europe while it struggles domestically.
United's victory helped Leverkusen, which won through Omer Toprak's second-half goal, as it condemned Shakhtar to a place in the Europa League after finishing third in the group.
Benfica joins Shakhtar in Europe's second-tier competition despite rallying from Edinson Cavani's 37th-minute opener for Group C winner PSG.
Lima converted a penalty on the stroke of halftime and Nicolas Gaitan scored from Maxi Pereira's diverted cross in the 58th, but the result wasn't enough for the Portuguese team because of the result across the continent in Greece.
Javier Saviola scored two goals for Olympiakos but was shaking his head in the 50th with the score at 1-1 when Anderlecht goalkeeper Silvio Proto saved his penalty. Saviola made up for that miss eight minutes later after swiveling to stab home his second for 2-1.
"Everything counts more in the Champions league: scoring, winning, celebrating," Saviola said. "So this is a great moment."
Proto stopped another penalty before being the third Andrlecht player sent off three minutes into stoppage time. Substitute Alejandro Dominguez beat outfield player Aleksandar Mitrovic — who filled in for Proto.
After a slow start, Madrid is certainly showing its mettle as a title favourite. The team extended its unbeaten run in all competitions to nine games, despite Ronaldo also having a second-half penalty saved.
Luka Modric got nine-time champion Madrid going with an exquisitely taken shot from just outside the area in the 25th, and Madrid never looked back with Ronaldo, Gareth Bale and Karim Benzema running the attack.
"Today I wanted to score, like every game. Every goal is important to help the team win and today it was extra special to break the record," said Ronaldo, who had been sidelined over two weeks with a hamstring injury. "But I don't think about records. The principal objective is to win trophies."
Madrid topped Group B with 16 points. Juventus needs just a draw against Galatasaray to advance, while the Turkish club needs a win.
Also in Group D, substitute Tomas Wagner volleyed home a 90th-minute winner as Viktoria Plzen sealed its place in the Europa League with a 2-1 victory against nine-man CSKA Moscow.
Ahmed Musa headed CSKA ahead in the 65th but Daniel Kolar nodded home an equalizer after Alan Dzagoev was red carded. CSKA midfielder Pontus Wernbloom was sent off moments after Wagner ensured coach Pavel Vrba's last Champions League game in charge of the club before he takes over the Czech Republic was a memorable one.
Each of the eight football grounds unveiled a banner that read "Madiba, The World Will Never Forget" before kickoff in honour of former South Africa president Nelson Mandela, who died on Thursday at age 95.
Follow Paul Logothetis on Twitter: www.twitter.com/PaulLogoAPSuggest a correction