Barcelona and Sporting advanced to the Champions League knockout stage while Inter Milan and Chelsea missed the chance to guarantee their places on Tuesday.
A 1-1 draw at home to Basel was enough for Barca to qualify from Group C alongside Portugal's Sporting, who beat Ukraine's Shakhtar Donetsk 1-0 thanks to Brazilian striker Derlei's 73rd-minute strike.
Tuesday night's results
Anorthosis 3 - 3 Inter Milan
AS Roma 3 - 1 Chelsea
Barcelona 1 - 1 Basel
Cluj 1 - 2 Bordeaux
Liverpool 1 - 1 Atlético M
Marseille 3 - 0 PSV
Sporting 1 - 0 S. Donetsk
W. Bremen 0 - 3 Panathinaikos
Substitute Lionel Messi put the Spaniards en route to the next phase when he fired the home side in front in the 62nd minute, though Basel gave the Primera Liga leaders a fright with an equaliser from Eren Derdiyok eight minutes before the end.
"It took us a bit of effort to get into the match and exert our superiority," Barca coach Pep Guardiola said in a television interview. "But we have qualified for the last 16 and that's great news."
In the other matches, last season's runners-up Chelsea fell 3-1 at AS Roma and Serie A champions Inter needed an 80th-minute header from striker Julio Cruz to salvage a 3-3 draw in Cyprus against a resilient Anorthosis Famagusta.
Liverpool, the 2005 champions, relied on a controversial stoppage-time penalty by captain Steven Gerrard to secure a 1-1 home draw with Atletico Madrid and remain level on eight points with the Spaniards at the top of Group D.
Inter's draw, combined with Panathinaikos's 3-0 win at Werder Bremen, left Group B wide open with two matches remaining. The Italians are top on eight points from four games, Anorthosis have five, Panathinaikos four and Werder three.
Mario Balotelli and Marco Materazzi put Inter ahead twice against Famagusta, but a string of defensive errors allowed Cedric Bardon and Georgios Panagi to equalise twice.
Another poor clearance allowed Nikolaos Frousos to fire the home side in front five minutes after the break before substitute Cruz saved the Serie A side's blushes.
"There were incredible individual errors. They really were gifts even if Christmas is still a way off," Inter coach Jose Mourinho told reporters.
Group A has a similarly tight look to it, with Chelsea on seven, one more than Roma and Girondins Bordeaux who beat CFR Cluj 2-1. The Romanians are still in contention with four points.
Defender Christian Panucci put Roma ahead before Mirko Vucinic struck twice at the start of the second half to end the Italian club's five-game losing streak.
"It's a result that gives us a little breather, a little tranquillity," Roma coach Luciano Spalletti told a news conference.
The Londoners pulled one back through captain John Terry in the 75th before having midfielder Deco sent off for a second yellow card five minutes later.
Despite the defeat Chelsea manager Luiz Felipe Scolari remains confident his side will progress.
"If we win one more game we are there. We'll have 10 points," he said.
After their draw, Liverpool and Atletico are favourites to progress from Group D where Olympique Marseille and PSV Eindhoven are five points behind after the French side defeated their Dutch opponents 3-0.
The Spanish side thought Maxi Rodriguez's 37th minute strike had secured the win, but Gerard converted from the spot after he was challenged in the box by Mariano Pernia and Swedish referee Martin Hansson awarded a debatable penalty kick.
"I was a long way from the incident to appreciate it fully," Atletico assistant coach Ignacio Ambriz said.
"It just shows how quickly things change in football. One minute we are in the next phase and suddenly that happens.
"We just have to carry on playing."