Roman Shirokov scored a hat trick Tuesday to put Zenit St. Petersburg on the brink of the Champions League group stage, while former European champions AC Milan and PSV Eindhoven are locked at 1-1 in their playoff.
Shirokov's treble came as Zenit easily overcame Pacos Ferreira 4-1 in their first leg.
At Eindhoven, Stephan El Shaarawy headed seven-time European champion Milan ahead after 15 minutes but Tim Matavz nodded in equalizer on the hour.
Tuesday's other matches saw teams claim two-goal advantages going into next week's second legs.
Kazakhstan champion Shakhter Karagandy stunned Scottish club Celtic 2-0, Real Sociedad won at Lyon by the same score and Viktoria Plzen beat Maribor 3-1 in the Czech Republic.
A further 10 clubs are in action on Wednesday as they chase a spot in the lucrative 32-team group stage, which starts in September.
Zenit can already start glancing ahead to the draw in Monaco later this month.
Shirokov, the Russia midfielder, took 27 minutes to find the net in Portugal, striking into the bottom of the net from Danny's cross.
Although Andre Leone volleyed Pacos Ferreira level in the 58th, Shirokov was on target again from close range at the back post two minutes later to restore Zenit's lead.
After Aleksandr Kerzhakov's free kick went off the crossbar and in off goalkeeper Matias Degra in the 85th, Shirokov completed his hat trick in style in the 90th, blasting the ball into the top right corner.
It was a far tighter encounter in the Netherlands as Milan and PSV played out the night's only draw.
PSV gifted Milan possession for the opener, with Ignazio Abate seizing the ball from Memphis Depay before whipping in a cross that El Shaarawy met with a free header.
But the 1988 European Cup winner leveled on the hour, with Jeffrey Bruma unleashing a dipping, swerving shot that goalkeeper Christian Abbiati spilled, and Matavz was alert to pounce and send a downward header into the net.
In Astana, Shakhter Karagandy closed in on a spot in the group stage for the first time with its victory over Celtic, the Scottish champion which beat Barcelona on its run to the Champions League last-16 last season.
Andrei Finonchenko put the hosts ahead after seizing on slack defending in the 12th minute, and Sergei Khizhnichenko headed in another in the 77th in Astana.
Celtic had come close to equalizing in the 19th when Kris Commons hit the crossbar with a powerful strike that bounced down close to the line.
It was unclear from TV replays whether the ball crossed the line, and UEFA has rejected the use of goal-line technology to adjudicate on such unclear situations.
Lyon has an uphill task advancing after Antoine Griezmann's acrobatic goal and Haris Seferovic's volley put Real Sociedad in control.
Lyon's troubles deepened in the 75th when Milan Bisevac was sent off after being shown a second yellow card.
It was an easier night for Czech side Viktoria Plzen, which took the lead against Maribor after just eight minutes through Marian Cisovsky.
Vladimir Darida and Michal Duris extended the hosts' lead in the second half, while Ales Mejac pulled a goal back for the 11-time Slovenian champions.