MADRID -- Comeback kings Barcelona and Galatasaray battled through Tuesday to the quarter-finals of the Champions League by eliminating AC Milan and Schalke 04.

Barca rediscovered its old swagger to thrash Milan 4-0 in front of a delighted Camp Nou, with two goals from Lionel Messi and one apiece from David Villa and Jordi Alba.

Barca went through on a 4-2 aggregate after losing 2-0 three weeks ago in Milan.

Galatasaray sprung the surprise of the round of 16 so far by battling out a spirited 3-2 win at Schalke 04, with crucial away goals from Hamit Altintop, Burak Yilmaz and Umut Bulut.

The Turkish team went through 4-3, after a 1-1 first-leg draw in Istanbul.

The capacity 94,000 crowd in Barca's Camp Nou was looking to Messi to lead the fightback after the meltdown in Milan, and the FIFA World Player did not disappoint them.

He opened the scoring after just five minutes with a high drive from his left foot, after taking a short pass from playmaker Xavi.

Milan's only clear chance to silence the Camp Nou came in the 38th minute, but M'Baye Niang hit the post when clean through in front of keeper Victor Valdes.

A relieved Barca celebrated by immediately going up 2-0, with Messi taking a pass from Andres Iniesta and scoring with a low, near-post drive.

Villa made it 3-0 10 minutes into the second half with a delightful left-foot curler, after being set up down the right by the influential Xavi.

Milan battled to score what would have been a crucial away goal but failed to create more clear chances.

Alba completed the rout two minutes into stoppage time by culminating a quick break engineered by Messi and Alexis.

In Gelsenkirchen, Galatasaray showed its quality and character by coming from behind to score a memorable 3-2 win.

The game started perfectly for Schalke as Roman Neustadter made it 1-0 after 17 minutes from close range, after the Turkish defense had made a mess of clearing a corner.

Galatasaray's fightback started in the 38th minute, when Hamit Altintop made it 1-1 with a fierce, 25-meter drive, which screamed in off the post.

Schalke were thrown out of its rhythm by the equalizer, and Yilmaz gave Galatasaray the lead just before half-time after being played through by Albert Riera.

Yilmaz' goal left Schalke needing to score twice. Michel Bastos made it 2-2 in the 63rd minute after a shot from Marco Hoger had hit the Turkish crossbar.

Schalke then laid siege to the Galatasaray goal, but the Turkish defense remained calm and firm.

In injury-time, with the hosts pouring forward and leaving gaps at the back, supersub Bulut made it 3-2 after a quick, precise break.

In Friday's quarter-final draw, Barca and Galatasaray will join Real Madrid, Juventus, Borussia Dortmund and Paris Saint-Germain, who qualified last week.

On Wednesday, Malaga will be trying to overturn a 1-0 first-leg deficit at home to FC Porto, while Bayern Munich will be defending the 3-1 lead it took three weeks ago in Arsenal's Emirates Stadium.

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