Holders Bayern Munich clinched a place in the Champions League knockout stages by beating Viktoria Plzen.
Mario Mandzukic's goal gave the German side their fourth win out of four in Group D, and sent them through along with second-placed Manchester City.
But Real Madrid could not seal their progress from Group B after a draw with Juventus and Group C leaders Paris St-Germain were held by Anderlecht.
Atletico Madrid can reach the last 16 by beating Austria Vienna on Wednesday.
There were no goals in Group A on Tuesday night, with Real Sociedad holding Manchester United and Shakhtar Donetsk and Bayer Leverkusen drawing 0-0 after the German side's goalkeeper Bernd Leno made a series of fine saves.
Leaders United failed to get the win they needed in Spain to reach the last 16 but a victory for the English side in their next game against Leverkusen will put them through.
Leverkusen's superior head-to-head record with Shakhtar means they will progress if they take four points from their last two games, at home to United and away to Real Sociedad.
Four points could also be enough for Shakhtar. If the Ukraine side beat Real Sociedad and Leverkusen beat United in the next round of fixtures, they would qualify ahead of David Moyes's side with a 2-2 draw at Old Trafford.
Sociedad have only one point from four games but can still go through if they win their final two group games and United beat Leverkusen and get at least a draw with Shakhtar.
Real Madrid drew 2-2 with Juventuson Tuesday but need one more point to be sure of qualification.
Even if they lose to Copenhagen and Galatasaray in their next two games, Real are unlikely to be denied a place in the last 16.
Copenhagen and Galatasaray would need to both beat Juventus and overturn Real by huge margins to outweigh the 4-0 and 6-1 defeats they suffered respectively in their first meetings with the Spanish giants.
If Juventus lose to Copenhagen next time out they will be eliminated. A draw would keep them in the competition, but leave them at the mercy of other results in the final round of matches. Victory in their last two matches would take them above both Copenhagen and Galatasaray and into the last 16.
Should Copenhagen and Galatasaray finish level on points in second position, the Turkish side would progress after winning 3-1 at home and losing by the one goal, Daniel Braaten's impudent backheel, in Denmark on Tuesday night.
Zlatan Ibrahimovic salvaged a draw for Paris St-Germain against Anderlecht as the French champions were made to wait for a Champions League last-16 spot.
Demy De Zeeuw put Anderlecht ahead after 68 minutes but Ibrahimovic levelled almost immediately, poking home at the second attempt after his first effort hit the post.
PSG will qualify if they beat Olympiakos in their next game on 27 November.
Olympiakos have a superior head-to-head record against Benfica so need four points to be sure of their progress. After going to Paris, they host Anderlecht on 10 December.
Four points could also be enough for Benfica if they beat Anderlecht and Olympiakos lose their last two games.
Anderlecht need to beat Benfica and Olympiakos and hope PSG beat Olympiakos and get at least a draw against Benfica.
Bayern Munich and Manchester City are through to the last 16, with the German side sitting top of the group with a 100% record.
Bayern equalled Barcelona's Champions League record of nine straight wins by beating Viktoria Plzen on Tuesday.
Bastian Schweinsteiger hit the post and Plzen keeper Matus Kozacik made several good saves before Mario Mandzukic headed home Philipp Lahm's cross in the second half.
Either City or Bayern could still finish top but the only other thing to play for is the Europa League spot for the team finishing third.
That is between CSKA Moscow, whose only points so far have come from a win over Plzen, and the Czech champions who are bottom after losing all their matches.
Chelsea can move clear at the top of Group E if they beat Schalke, who are currently level on points with the Blues.
Basel will move into second place if they beat winless Steaua Bucharest and the game at Stamford Bridge ends in a victory for either team.
Arsenal are level on points with Borussia Dortmund and Napoli in a three-way tie at the top of the group.
Dortmund take on Arsenal on Wednesday, with the German side chasing what would be an eighth successive home Champions League win, having never lost against English opposition at the Westfalenstadion.
Napoli host Marseille, who are bottom after losing their first three games and have only faint hopes of qualifying. Only Newcastle, in 2002-03, have qualified for the next stage after losing their first three games.
Atletico Madrid have won their first three group games and can secure a place in the last 16 if they beat Austria Vienna on Wednesday.
Behind them, the battle is on for second place, with Zenit St Petersburg a point ahead of their next opponents, FC Porto.
Barcelona will increase their lead at the top of the group if they beat AC Milan on Wednesday.
Celtic can move into second place if they beat bottom side Ajax and Barca win.