Chelsea and AC Milan took purposeful strides towards the Champions League semi-finals with victories by two clear goals in their home quarter-final first legs on Wednesday.

Chelsea beat Bayern Munich 4-2 at Stamford Bridge, the Germans staying in the tie with a controversial stoppage-time penalty, while Milan beat city rivals Inter 2-0 at the San Siro stadium the two clubs share.

Liverpool beat Juventus 2-1 at Anfield and PSV Eindhoven struck a late equaliser to draw 1-1 at Olympique Lyon in Tuesday's first legs.

Michael Ballack's [Images] 93rd-minute penalty for Bayern ensured there would be plenty to play for in Munich after Chelsea had looked on course for the last four.

The runaway Premier League leaders took the field without any guiding words from Jose Mourinho as their manager was banned from the touchline and decided to watch the game from a "peaceful place".

It was anything but quiet at the West London [Images] ground after four minutes, however, when Chelsea took a fortunate lead with a deflected long-range shot by Joe Cole.

Bayern levelled in the 52nd minute when halftime substitute Bastian Schweinsteiger tapped in after goalkeeper Petr Cech failed to hold a Ze Roberto shot.

Chelsea, semi-finalists last season and impressive conquerors of Barcelona in the last round, regained the lead on the hour when inspirational England [Images] midfielder Frank Lampard [Images] seized on a Didier Drogba [Images] flick to score from just outside the box.

Lampard, a front runner for England's Footballer of the Year award, then produced an even better finish as he spun through 360 degrees before sending another left-footer flashing beyond Kahn.

DIRECT APPROACH

The Bundesliga leaders, who knocked out Arsenal [Images] in the last round, had no answer to Chelsea's direct approach, and the hosts looked to have completed a great night nine minutes from time when Drogba smashed in the fourth.

Munich were handed a lifeline, however, when Ballack went down under the challenge of Ricardo Carvalho and got up to convert the penalty.

"At the moment I'm disappointed because of the last minute," Lampard told Sky Sports TV.

"Four-one would have been a great lead but 4-2 still is and we are in a good position."

Bayern coach Felix Magath recognised the importance of Ballack's penalty.

"At 4-1 we were almost out," Magath said. "Now we have a good chance to turn things round in the return."

The two Milan clubs met in the semi-finals two years ago with AC Milan advancing on away goals having drawn their "away" leg 1-1 after a goalless first leg.

Six-times champions Milan were the home side first again, thereby having 70,000 of the 80,000 tickets, but this time found the net twice.

The first came in first-half stoppage time when centre back Jaap Stam glanced in Andrea Pirlo's free kick for his first goal for the club.

Pirlo was also the provider of the second in the 74th minute as another tempting free kick was headed in from point-blank range by fit-again striker Andriy Shevchenko on his first appearance for nearly two months.

Milan were comfortably in charge in the second half although Inter, who had started well, hit the post late on through Greek substitute Giorgos Karagounis.

It will be Inter's turn to be the home team on Tuesday, when Chelsea will play in Munich.

The winners of the all-Milan tie will play Lyon or PSV in the semi-finals, while Chelsea or Bayern face Liverpool or Juventus.

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