Werder Bremen and Hapoel Tel Aviv look likely to reach the Champions League group stages after playoff wins.
Clemens Fritz, Torsten Frings and Claudio Pizarro scored in the second half to give Bremen a 3-1 win over 10-man Sampdoria, while Hapoel Tel Aviv won 3-2 at Salzburg for a crucial edge ahead of next week's second-leg matches.
Braga shocked Spain's Sevilla 1-0 in Portugal, Basel beat FC Sheriff 1-0 and Anderlecht drew 2-2 at Partizan Belgrade.
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Werder took to the pitch without Mezut Oezil for the first time at the Weserstadion after selling the German playmaker to Real Madrid this week, but still took the lead against Sampdoria in the 51st through Clemens Fritz.
Giampaolo Pazzini almost equalised when his shot across goal bounced off the far post and into the arms of stranded goalkeeper Tim Wiese.
Sampdoria's luck worsened when the referee finally tired of the Italian side's cynical defending and sent off Stefano Lucchini with a second yellow card for holding an opponent in the area.
Frings scored with the resulting penalty in the 67th and Pizarro completed the scoring for Bremen, bursting into the area after an exchange of passes and shooting past Gianluca Curci.
Pazzini gave Sampdoria some hope with a last-minute header from the edge of the six-yard box but Lucchini will be suspended for Tuesday's return match in Genoa, leaving the Italian side with a tough task to reach the Champions League for the first time.
With away goals counting double if scores are level after next week's second-leg matches, Hapoel Tel Aviv looks set to make the group stage after scoring three in Austria.
The Israeli team took the lead with a third-minute penalty scored by goalkeeper Vincent Enyeama and, after Nikola Pokrivac equalised midway through the first half, went 3-1 up by the 53rd through former Chelsea forward Ben Sahar and Itay Shechter.
Roman Wallner scored a 66th-minute penalty for Salzburg to give the Austrian side some hope.
The winners over two games earn places in the lucrative group stage and the losers drop into the second-tier Europa League.
Partizan Belgrade equalised twice to keep alive realistic hopes of edging Anderlecht to a spot in the group stages, but the Belgian side takes two away goals from defenders Guillaume Gillet and Roland Juhasz.
Sevilla won the Europa League under its previous guise of the UEFA Cup in 2006 and '07 but need to score at least once at their home Sanchez Pizjuan stadium after Brazilian striker Matheus headed in a 62nd-minute rebound to give Braga a 1-0 victory.
Basel beat Moldova's Sheriff 1-0 through Valentin Stocker's 54th-minute close-range header but missed a 90th-minute penalty when Vladislav Stoyanov saved Benjamin Huggel's spot kick.
Sheriff have been in the Champions League qualifying stages for 10 straight years but never reached the competition.
This is their second appearance in the third qualifying round, having entered the Europa League after losing to Olympiakos at this stage last season.
