England midfielder Steven Gerrard's first-half goal secured Liverpool's place in the last 16 of the Champions League as they beat Olympique Marseille 1-0 at Anfield.
From the same Group D, Atletico Madrid also made it through thanks to a 2-1 win over PSV Eindhoven behind closed doors at the Calderon.
Inter stumbled into the last 16 despite suffering a surprise 1-0 home defeat to Panathinaikos in a Group B match at the San Siro while the other Serie A side in action, Roma, edged closer to qualification thanks to a 3-1 away win at CFR Cluj.
A late Alou Diarra goal denied Chelsea an early ticket to the first knockout phase of the competition when last year's runners-up were held 1-1 at Bordeaux.
Liverpool skipper Gerrard scored with a far-post header in the 23rd minute from Xabi Alonso's deep cross to settle the issue.
Marseille failed to repeat the surprise 1-0 victory they recorded at Anfield last year that would have kept their hopes of qualification alive.
The French side did create plenty of chances with keeper Pepe Reina saving well from free-kicks by Taye Tawio and Hatem Ben Arfa.
Atletico were serving a one-match punishment from UEFA for the crowd problems that marred their 2-1 home victory over Olympique Marseille in October.
Simao Sabrosa and Maxi Rodriguez struck in the first half as Atletico dominated but PSV scored two minutes into the second half through in-form striker Danny Koervermans.
The Dutch side grew in confidence but Atletico held firm for the win despite some nervous moments near the end. Liverpool and Atletico Madrid have 11 points with one match remaining.
Anorthosis Famagusta's 2-2 draw with Werder Bremen means Inter go through because the Cypriots visit Panathinaikos in the last round of matches and both cannot finish above the Italian champions.
Jose Sarriegi tapped in on 69 minutes after goalkeeper Julio Cesar could only parry Giannis Goumas's towering header from a corner.
Stuttering Serie A leaders Inter have only played well in one Champions League match this term, the 2-0 win at Panathinaikos in the opening group game.
Werder came from two goals down to deny Cypriot newcomers Anorthosis from victory but it was not enough to prevent the Germans slipping out.
Substitute Nikos Nikolaou struck with a half-volley at a corner to put the home side ahead with just over an hour gone and Brazilian forward Savio made it 2-0 up soon afterwards.
Werder, needing a win to stay alive, pulled one back almost immediately when Diego lashed in a penalty and Hugo Almeida struck with a low volley three minutes from time to level things up.
The result gave Anorthosis six points from five matches and meant they still have a chance of making progress in their extraordinary debut campaign.
Bordeaux midfielder Diarra headed home from a Yoann Gourcuff corner with seven minutes remaining to cancel out Nicolas Anelka's 60th-minute opener.
Chelsea, who had Frank Lampard sent off in the 86th minute, are now second in Group A with eight points from five matches, one point behind Roma, who won 3-1 at CFR Cluj. Bordeaux are third on seven points and travel to Roma in two weeks' time with Chelsea hosting Cluj.
Matteo Brighi scored a goal in each half for Roma. He opened the scoring in the 11th minute after a defensive error and added his second in the 64th after a perfect assist from Rodrigo Taddei.
Francesco Totti converted a 22-metre free-kick to make it 2-0 in the 23rd minute but Yssouf Kone pulled a goal back seven minutes later.
Roma's victory made up for their shock 2-1 home defeat to Cluj in the group opener at the Stadio Olimpico in September.
Barca rout
Barcelona clinched top place in Group C when they crushed Sporting 5-2 in an action packed game in Portugal.
With the two teams having already qualified for the knockout stage, Barca took their points tally to 13 with one game still to play, four points ahead of the Lisbon team.
Thierry Henry opened the scoring for Barcelona in the 14th minute and three minutes later Barcelona doubled the lead with a goal by defender Gerard Pique in a scramble.
Messi converted a quick free-kick in the 50th minute then, between the 65th and 66th minutes, Sporting pulled back to 3-2 with goals by Miguel Veloso and Liedson before a Marco Caneira own goal made it 4-2.
Substitute striker Bojan Krkic added a fifth for Barca with a 73rd-minute penalty after he was brought down by keeper Rui Patricio who was sent off for the foul.