The Reds came into the final group stage match on Tuesday evening needing at least a draw to be sure of staying alive in the competition, reports Efe news. Playing in front of their supporters in Salzburg, the proud Red Bull side made Liverpool earn the three points with a minute of magic approaching the hour mark.
Naby Keita scored in the 57th minute on a play engineered by Trent Alexander-Arnold. Mo Salah struck seconds later to make it 2-0 for the visitors.
Liverpool win Group E with 13 points, 1 ahead of Napoli, who romped 4-0 over KRC Genk on Arkadiusz Milik's hat-trick and a goal by Dries Martens in the final stretch.
Valencia also faced a test on the road, travelling to Amsterdam for a showdown with Ajax, one of last year's Champions League semi-finalists.
Ajax started Match Day 6 atop Group H with 10 points, followed by Valencia and Chelsea with 8 points each.
Rodrigo's goal in the 24th minute turned out to be enough for Valencia to prevail 1-0 at Johan Cruyff Arena and the Spanish club can now look forward to their first appearance in the Champions knockout stage since 2012.
In London, Chelsea took a 2-0 lead over Lille in the first half on goals by budding star Tammy Abraham and Cesar Azpilicueta. The crowd at Stamford Bridge grew nervous when Loic Remy pulled one back for the visitors in the 78th minute, but the Blues hung on for the victory and punched their ticket for the round of 16.
Barcelona locked down first place in Group F on Match Day 5, leaving Borussia Dortmund and Inter Milan - both on 7 points - to battle for the second berth.
The Italian side faced the bigger challenge defeating Barcelona at Camp Nou.
With nothing at stake, Barcelona coach Ernesto Valverde rested captain Lionel Messi and several other starters, giving minutes to the likes of Carles Alena, Neto, Carles Perez, Jean-Clair Todibo and Moussa Wague.
One of the subs, Perez put the hosts up 1-0 in the 23rd minute, yet Romelu Lukaku equalized for Inter in the final minute of the first half.
The visitors chased furiously after the goal that would send them to the next round. And twice, they thought had it. But Lautaro Martinez saw two goals disallowed before 17-year-old Ansu Fati sealed the win for Barcelona with a strike in the 86th minute, becoming the youngest goal-scorer in Champions League history.
Dortmund, hosting last-place Slavia Prague, eked out a 2-1 win to grab the other round-of-16 spot.
In Group G, Lyon had to come from behind to salvage a 2-2 draw with group winners Red Bull Leipzig.
Tied with Lyon on points at the start of the day, Zenit St. Petersburg lost 0-3 to Benfica.
( With inputs from IANS )