Home striker Diego Milito netted on three minutes when he easily turned John Terry and fired in at the near post from six metres, prompting little reaction from Inter's former Chelsea coach Jose Mourinho who had promised not to celebrate.
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The Londoners dominated a thrilling game for long spells and Salomon Kalou deservedly equalised on 51 minutes with a 20-metre shot before Esteban Cambiasso soon put the hosts back ahead after his first shot was blocked.
Chelsea keeper Petr Cech was carried off on a stretcher in the second half with a calf injury but Carlo Ancelotti, who spent eight years at the San Siro as AC Milan coach, will be confident of turning the tie around in the second leg on March 16.
"It was a high-level Champions League game," Mourinho told ITV Sport. "I said to my players, 'they are not better than us, they are different to us'.
"Chelsea and Inter can both play better. This is the Champions League, it is difficult to fully express yourself because of the pressure."
Just like rivals AC Milan in their defeat by Manchester United on the same pitch last week, Serie A champions Inter got off to a good start.
CECH BEATEN
Thiago Motta threaded the ball forward and Samuel Eto'o miscontrolled it before strike partner Milito confirmed his excellent form this season by cutting in from the left and beating Cech at the near post.
Chelsea's heads failed to drop despite the vast roar from the Inter crowd and they were soon troubling keeper Julio Cesar, playing despite being shaken in a car crash early this week.
A Michael Ballack piledriver forced the Brazilian into his best save and Didier Drogba rattled the bar with a vicious free-kick.
Kalou, included on the left with Florent Malouda employed at left back, then had a strong shout for a penalty turned down on the stroke of halftime after a challenge by Walter Samuel five metres out.
The Ivorian had his reward after 51 minutes when Julio Cesar failed to stop his curling shot through a crowd of players.
Argentine Cambiasso then grabbed the winner, blasting in at the second attempt from the edge of the box.
"I think on the balance of play, possession, the shots we had, we were the stronger team," said Chelsea midfielder Frank Lampard.
"We knew they like to soak up pressure and they got the early goal which made it easier for them but we've got an away goal and with a performance like that in London we've got a great chance."
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