AC Milan kept their Champions League hopes alive with a 3-0 thrashing of Celtic that ended a miserable seven-game winless run and sent the Scottish side crashing out of Europe.
Ajax's 2-1 win over already qualified Barcelona means the Dutch champions and Milan will battle it out for the other place in the knockout stages out of Group H, while Celtic, who will finish bottom, head to the Nou Camp for the final group game with nothing but pride to play for.
Milan, who hadn't won away in Europe in almost a year, got off to the perfect start when Kaka found himself with time and space to head home a 12th minute corner.
The Hoops were left to rue a missed opportunity for Virgil van Dijk just after the break when Cristian Zapata increased Milan's advantage with a 49th minute tap-in.
Van Dijk had a goal ruled out for offside minutes later before Mario Balotelli ended Celtic's hopes when his strike made it 3-0 in the 59th minute as Milan became only the second side to defeat the hosts at home in the group stages of the Champions League.
The win leaves Milan in second spot on eight points -- a point ahead of Ajax - and eases the pressure on coach Massimiliano Allegri, who has come in for criticism following his side's poor domestic form that saw fans protest outside the San Siro following a 1-1 draw with Genoa at the weekend.
Allegri was clearly delighted with his side's victory.
"Technically I thought we were very good and we created some good chances," the under-fire Milan boss said.
"I am happy with the victory and we have to make sure we take this form into the domestic championship."
His Celtic counterpart Neil Lennon said the loss had been symptomatic of their Champions League campaign.
"We missed good chances and I'm really disappointed with the two goals we conceded from corners," the Celtic manager said.
"Realistically getting into the Champions League was fantastic for us and when the draw was made we knew it was going to be hard."
Celtic were without captain Scott Brown and Nir Biton due to suspension for the must-win match while Joe Ledley dropped to the bench. Winger James Forrest, who earlier on Tuesday was arrested in connection with two alleged public indecencies, started the match.
AC Milan arrived in Glasgow with a lengthy injury list, defender Philippe Mexes and midfielder Sulley Muntari joining Stephan El Shaarawy, Mattia De Sciglio and goalkeeper Marco Amelia in being ruled out.
Celtic were presented with a great early chance when Charlie Mulgrew's effort fell kindly to Beram Kayal inside the box but the midfielder couldn't adjust his feet quickly enough and Zapata recovered to make a last-ditch saving tackle.
The Hoops were left to rue that miss moments later when Brazil star Kaka slipped marker Van Dijk to easily head home Valter Birsa's corner from close range.
Celtic were again the recipients of a ball breaking kindly to them in the Milan box but this time Mulgrew sent his weak shot straight at Christian Abbiati.
The Hoops should have been level in the 47th minute. Mulgrew's cross found Van Dijk eight yards out but he sent his volley straight at Abbiati when he had the whole goal to aim for.
The Dutch defender's misery was compounded two minutes later when Milan doubled their advantage.
Birsa's deep corner was fired back across goal by substitute Antonio Nocerino for Zapata to side-foot home from close range.
Any hope Celtic had was ended in the 59th minute when Balotelli made it 3-0.
The Italian striker collected a long ball from Riccardo Montolivo and shrugged off the challenge of Efe Ambrose before sending an angled shot past helpless goalkeeper Fraser Forster.