Twice European champions Porto won 1-0 at CSKA Moscow in another of the round-of-16 first leg ties and Benfica completed an excellent night for Portugal with a 2-1 win over visiting Paris Saint-Germain.
Former AC Milan and Chelsea striker Andriy Shevchenko set Dynamo Kiev on the way to a 2-0 home win over big-spending Manchester City and wasteful Ajax Amsterdam were beaten 1-0 at home by Spartak Moscow.
Brazil striker Nilmar came off the bench to score twice, including a stoppage-time winner, in Villarreal's 3-2 triumph at Bayer Leverkusen on a night when South Americans were very much in evidence.
Braga dominated the first half against visitors Liverpool and Portuguese Alan converted his spot-kick in the 18th minute after defender Sotiris Kyrgiakos tripped Brazilian Mossoro.
Manager Kenny Dalglish was angry with Liverpool's first-half display during which Silvio also hit the woodwork for Braga.
"The first 35 minutes we were terrible," said the Scot, who was without injured captain Steven Gerrard and ineligible forward Luis Suarez. "The penalty summed up the way we were approaching the game.
"I think at 1-0 we've still got a chance but if we play like we did at the start of the first half at Anfield we haven't got any chance."
CSKA DEFEAT
CSKA, playing their 11th match in this season's competition, slumped to their first defeat after a superb effort from Porto's Colombian midfielder Fredy Guarin who turned his marker and scored from 25 metres in the 70th minute.
In Lisbon, Uruguayan Maxi Pereira and Argentine Franco Jara were on target as Benfica came from behind against Paris Saint-Germain, Peguy Luyindula having put the French side ahead.
Shevchenko, 34, looked as sharp as ever when he turned in Andriy Yarmolenko's inviting cross in the 25th minute to put Dynamo Kiev ahead against Roberto Mancini's team.
Oleh Gusev increased the Ukrainians' lead 13 minutes from time.
"I think we made two mistakes, big mistakes for the goals, I think we can't concede mistakes like this in this game," said Manchester City manager Roberto Mancini.
"We had control of the game, they played on the counter attack. I'm frustrated because we conceded two goals."
Brazil striker Nilmar came off the bench in the 69th minute for Villarreal at Leverkusen and scored within a minute to put his team 2-1 ahead.
Gonzalo Castro levelled for the Bundesliga team two minutes later, only for Nilmar to break clear in the fourth minute of added time to slot home the winner.
Michal Kadlec had fired Leverkusen ahead with a 30-metre shot before Giuseppe Rossi replied for Spain's last survivors as the first-half ended 1-1.
Four-times European champions Ajax wasted a host of chances, with Siem de Jong the main culprit, before Alex, another Brazilian, sna
