Lionel Messi celebrates in Wednesday's 4-0 win at Barcelona. ((Manu Fernandez/Associated Press))

Inspired by the brilliance of Lionel Messi's two goals, defending champion Barcelona beat Stuttgart 4-0 on Wednesday to power into the Champions League quarter-finals as Bordeaux defeated Olympiakos 2-1 to also advance.

Pedro Rodriguez and Bojan Krkic also hit the target as Barcelona went through 5-1 on aggregate despite missing injured midfielder Xavi Hernandez.

Leading 1-0 from the first leg, Bordeaux scored a goal in the fifth minute from a bending free kick by Yoann Gourcuff. Kostas Mitroglou replied for Olympiakos with a long-range drive but Marouane Chamakh added an acrobatic headed goal for a 3-1 overall victory.

Barcelona and Bordeaux join Manchester United, Arsenal, Bayern Munich, Lyon, Inter Milan and CSKA Moscow in the last eight. The draws for the quarter-finals and semifinals will take place on Friday at UEFA headquarters at Nyon in Switzerland.

Three English clubs have made it to the semifinals in the past two seasons, but only Manchester United and Arsenal have survived to the last eight this time. With no seeding system to keep them apart, they could be drawn to face each other. The same applies to French clubs Lyon and Bordeaux.

Inter Milan is trying to win the title for the first time since 1965 and is coached by Jose Mourinho, who won it with FC Porto in 2004 and knocked out his former club Chelsea on Tuesday. Arsenal, Lyon, Bordeaux and CSKA have never won the competition.

Even without Xavi, who was out with a calf injury, Barcelona had too much talent for Stuttgart at Camp Nou.

Playing at his magical best, Messi collected a ball from Yaya Toure in the 13th minute and ran at the Stuttgart defence before firing a 20-meter, left-footed shot into the top corner of the net.

"He was so decisive," Barcelona coach Pep Guardiola said of Messi. "Every great has a tendency to influence his team, like [Michael] Jordan with the Bulls. He's the best. We wouldn't trade him for anybody."

Pedro added the second in the 22nd minute when he tapped in a low cross from Toure in a move started by Messi.

'His ability is incredible'

Messi made it 3-0 in the 60th when he turned a defender just outside the area and fired a low shot past goalkeeper Jens Lehmann.

The Argentina star, who scored three times against Valencia in the Spanish league on Sunday, should have had another hat trick in the 86th minute when he dribbled past three men but rolled the ball wide of goal.

"His ability is incredible when you consider his age," Stuttgart coach Christian Gross said of the 22-year-old Messi. "I think it's fair to compare him to [Diego] Maradona."

Began added the fourth with his first touch in the 89th minute after receiving a pass from fellow substitute Zlatan Ibrahimovic.

While Mess's dribbling and shooting mesmerized his opponents in Barcelona, Bordeaux's big weapon was Gourcuff's spectacular free kicks.    From wide on the left in the fifth minute, he curled his shot over the goalkeeper and in off the inside of the far post. Gourcuff also hit the bar and post with a near identical free kick in the final minute of the first half.

Olympiakos' Matt Derbyshire put the ball in the net but it was ruled out for offside. The English striker was sent off in the 60th minute after his second yellow card.

Despite being down to 10 men, the Greek champions hit back and substitute Kostas Mitroglou equalized on the night with a powerful right-footed shot in the 64th minute. The game became 10 against 10 when Bordeaux's Alou Diarra was sent off for a lunging tackle five minutes later.

That meant a second goal for Olympiakos would have put the Greek club through on away goals. But Chamakh jumped highest to head home a left-wing cross in the 89th minute, tumbling over his opponent as the ball flew into the net.

Bordeaux has now reached the last eight of European football's most prestigious club tournament for the first time since 1988.

Bordeaux coach Laurent Blanc said that having two teams in the last eight was a sign of a revival in domestic French football.

"You can think that because of the teams now qualified for the Champions League quarter-finals, and those doing well in the Europa League, that this proves that French football is in good shape," Blanc said.

"But to confirm this we will have to see how this develops over time to see if this can happen again, and to see how regularly French teams get through to the quarter-finals."

In Tuesday's games, Inter won 1-0 at Chelsea to advance 3-1 overall and CSKA reached the quarter-finals for the first time by beating Sevilla 2-1 and 3-2 on aggregate.