Two-time European champions Benfica won and Lazio were held to a home draw on Tuesday in the third qualifying round of the Champions League.
Benfica, who won Europe's most prestigious competition in 1961 and 1962, beat FC Copenhagen 2-1, while Lazio had two men sent off and drew 1-1 with Dinamo Bucharest in Rome.
Rangers beat visiting Red Star Belgrade 1-0 through a 90th-minute goal, while Valencia overwhelmed Sweden's Elfsborg 3-0.
The winners over two matches will advance to the Aug. 30 draw for the lucrative group stage, where they will be joined by Europe's top teams such as AC Milan, Manchester United, Real Madrid and FC Barcelona.
Rui Costa scored Benfica's winner -- his second of the night -- in the 86th minute to give his side a crucial lead over FC Copenhagen heading into the second match of the two-leg meeting on Aug. 29.
Costa put the Portuguese team ahead in the 25th minute, running at the defense and unleashing a powerful low drive past goalkeeper Jesper Christiansen's outstretched right hand.
But Benfica paid for their clumsy defending 10 minutes later when Atina Hutchinson poked the ball into the corner from close range.
Benfica coach Fernando Santos took off injured central defender Luisao before halftime and sharpened his attack by handing Freddy Adu his European debut.
With time running out, Santos brought on two other strikers but it was midfield veteran Rui Costa who struck from outside the area to seal the win.
Lazio, who are trying to return to the group phase for the first time since the 2003-2004 season, fell behind to Dinamo Bucharest in the 22nd minute when Ionel Danciulescu headed a long cross past 43-year-old goalkeeper Marco Ballotta and into the top corner of his net.
Ballotta has claimed Lazio's starting job while newly signed Argentine keeper Juan Pablo Carrizo attains EU citizenship. Angelo Peruzzi retired after last season.
Lazio were playing a man down when Dinamo scored, not having replaced defender Sanchez Cribari, who was stuck in the face while challenging for a high ball three minutes earlier.
Lazio bombarded Dinamo's goal in the first half, but could not beat goalkeeper Bogdan Lobont, who even blocked a penalty kick by Tommaso Rocchi in the 38th minute.
Massimo Mutarelli equalized for Lazio with a header from the center of the area in the 54th minute, but Lazio finished with nine men when Valon Behrami was shown a direct red card for a hard sliding tackle in the 73rd minute, and Mutarelli picked up a second yellow in the 86th minute.
Dinamo defender Dorin Goian was ejected for a second yellow in the 90th minute.
Several fans were injured in violent clashes outside the stadium in Rome before the match, local reports said.
At Valencia's Mestalla stadium, goals from Vicente Rodriguez, David Silva and Fernando Morientes comfortably paced the Spanish past Elfsborg.
Valencia dominated possession from the start and despite Elfsborg goalkeeper Johan Wilan thwarting chances by David Villa and Emiliano Moretti in the first 15 minutes, his save of Villa's shot in the seventh minute was wasted when Rodriguez converted the rebound.
Two more chances in the first 10 minutes of the second half also were wasted by Valencia, but Silva then outleapt two defenders in the 59th minute to head home Joaquin's cross for the second before Morientes headed in another cross from the right winger 11 minutes later for the finale.