Former European champions Steaua's 10 men held Copenhagen 1-1 to progress as Group E winners on 11 points.
Stuttgart, who lost 1-0 to Molde, finish in second on eight and level with the Danes but the Germans progressed owing to a better head-to-head record. Davy Angan scored the only goal in first half injury-time.
Steaua were reduced to 10 men in the 49th minute when Cristian Tanase was sent off but took the lead through Raul Rusescu after 72 minutes, Copenhagen only capitalising on their advantage late on but it was to no avail.
Five-times European champions Liverpool survived a late scare to move into the last 32 with a 1-0 win over Italian side Udinese while Tottenham beat Panathinaikos 3-1 to take the final Group J slot behind winners Lazio who breezed to a 4-1 win at Maribor.
Basel's 0-0 draw at Group G's top club Racing Genk ensured Hungary's Videoton, whose match at Sporting was postponed to Friday due to a waterlogged pitch, went out.
The game was played on Friday, when Sporting ended their campaign on a high after sealing their first win of the tournament 2-1 over the Hungarian visitors.
Bordeaux won the battle for top spot over Newcastle United in Group D, the French club running out 2-0 victors to reach 13 points with the Premier League side on nine.
Vaclav Prochazka scored the only goal of the game in the 26th minute as Viktoria Plzen beat holders Atletico Madrid to qualify as Group B winners.
Both sides had already qualified for the next stage but Plzen's win helped them move above the Spaniards into pole position on 13 points. Atletico had Brazilian Diego Costa sent off in injury time.
Also in Group B, Hapoel Tel Aviv claimed their first win with a 2-0 victory over Academica in Israel. Victor Merey and Hanan Maman scored in the second half, although both sides had already been eliminated.
Anzhi Makhachkala scraped into the knockout stages of Group A despite falling to a 3-1 defeat at Young Boys. Goals from Gonzalo Zarate, Moreno Costanzo and Alexander Gonzalez gave Young Boys victory over Anzhi, who replied through Odil Akhmedov and had Lacina Traora sent off.
In Group D, goals from Goncalo Abreu and Heldon were enough to see Maritimo home with a 2-1 win over Club Brugge, who replied through a Lior Refaelov penalty.
Having already confirmed their place at the top of Group C, Fenerbahce were hammered 3-0 at home by runners-up Borussia Monchengladbach, for whom Tolga Cigerci, Mike Hanke and Luuk de Jong got on the scoresheet.
Cypriots AEL Limassol finished their Group C campaign with their first win, 3-0 over Marseille, with goals from Orlando Sa, Edmar and Dossa Junior. Two goals from Roman Zozulya and further strikes from Nikola Kalinic and Sergey Kravchenko saw Group F winners Dnipro finish with an emphatic 4-0 home win over AIK.
Second-placed Napoli fell 3-1 at home to already-eliminated PSV, despite taking an 18th-minute lead through Edison Cavani. A hat-trick from PSV's Tim Matavz helped the Dutch side finish in style.
With both sides having already qualified from Group L, Levante and Hannover played out a 2-2 draw in Spain, with the Germans blowing a 2-0 lead but still taking the point they needed to top the group.
Lars Stindl and Didier Ya Konan put the visitors in front before the half-hour mark but the hosts hit back after the break with Angel pulling one back on 49 minutes and Vicente Iborra hitting an injury-time leveller. Also in Group L, Helsingborg won 3-1 at FC Twente in a match between two sides who were already eliminated.
Group H winners Rubin Kazan settled for a 1-1 draw at Partizan Belgrade. Aleksandar Markovic put the hosts ahead on 53 minutes and Salomon Rondon equalised for the Russians five minutes later.
Also in Group H, Inter Milan, already assigned the runners-up position, drew 2-2 at home to Neftci. Marko Livaja's two goals for Inter were cancelled out first by Rashad Sadygov, then by Nicolas Canales one minute from time.
With Group K already settled, Deni Alar's 13th-minute goal gave Rapid Vienna their first points with a 1-0 win over Metalist Kharkiv. Runners-up Bayer Leverkusen beat Rosenborg 1-0 with a goal from Julian Riedel.
Goals from Mouhamadou Sarr and Yassine Benzia gave Group I winners Lyon a 2-0 win over Hapoel Kiryat Shmona, while second-placed Sparta Prague played out a goalless draw at Athletic Bilbao.
European champions Chelsea, knocked out of the Champions League on Wednesday, head the eight teams who failed to qualify from Europe's top-tier competition this week to make up the 32 in the draw on December 20.