Russian champions Zenit St Petersburg, who won all their group stage games, lost to a stoppage-time goal at Young Boys in another round of 32 first leg tie.
However, their compatriots Spartak Moscow were on the right end of a comeback away to Swiss opponents as they bounced back from 2-0 down to win 3-2 at FC Basel.
Liverpool could not field new striker Luis Suarez under UEFA regulations, with his former club Ajax also playing in the competition, and failed to find the target as they drew 0-0 at Sparta Prague.
"It wasn't a classic," Kenny Dalglish told Britain's Channel Five television after managing Liverpool in Europe for the first time.
"The onus was on them to try to put us under a wee bit of pressure. We made a couple of opportunities as well. On the night, 0-0, fair enough. I'm happy with that."
Ajax won 3-0 at Anderlecht while fellow Dutch side Twente Enschede were among several teams who endured freezing conditions in eastern Europe, beating Rubin Kazan 2-0 in Moscow where the temperature hovered around minus 15 Celsius.
Lille were held 2-2 at home after a late rally by PSV Eindhoven in a meeting of the French and Dutch league leaders.
Porto, beaten only once in 34 outings in the Portuguese League and Cup and Europa League this season, went ahead in the 58th minute when Rolando stabbed home after a free-kick.
Sevilla striker Frederic Kanoute levelled in the 65th, also from a free-kick, before Colombia midfielder Guarin stole the win with five minutes left as Porto made a happy return to the scene of their 2003 UEFA Cup final win over Celtic.
Stuttgart's impressive European form has been in marked contrast to their shaky Bundesliga performances this season and Martin Harnik gave them a first-half lead in Lisbon.
But Benfica hit back as Paraguay striker Oscar Cardozo, one of eight South Americans in the team, equalised in the 70th and Argentine Franco Jara got the winner with nine minutes left.
ZAMBIAN HERO
Zambian striker Emmanuel Mayuka was the Young Boys hero, scoring in the third minute of added-time on the Stade de Suisse's artificial pitch to snatch a 2-1 win over 2008 UEFA Cup winners Zenit. The 20-year-old only came on in the 83rd.
Belgian international Nicolas Lombaerts had given Zenit a first-half lead with a header from a corner.
Senad Lulic levelled with a solo effort within a minute of the restart and the Russians had substitute Vladimir Bystrov sent off for a second bookable offence 20 minutes from time.
It was the other way round at FC Basel where Alex Frei and Marco Streller gave the Swiss champions a 2-0 half-time lead against Spartak Moscow in a clash of two sides parachuted into the competition after being knocked out of the Champions League.
