Meanwhile, hapless Celtic were knocked out of the competition for a second time in three weeks.
Brahimi, who shone for Algeria in the World Cup, curled in a majestic free-kick and set up a second goal for Jackson Martinez to give Porto a 2-0 win over Lille in their play-off round second leg tie.
Hulk scored twice, converting a penalty and then barging his way through the Standard Liege midfield, as Zenit beat the Belgians 3-0 despite playing the second half with 10 men.
APOEL Nicosia, 4-0 winners over Aalborg, and Belarus champions BATE Borisov, who beat Slovakian counter-parts Slovan Bratislava 3-0, also qualified.
Porto went ahead in the 49th minute when new signing Brahimi curled a superb effort over the Lille wall from 25 metres.
He followed that up by splitting open the Lille defence and finding Colombia forward Jackson Martinez who swept home a first-time effort in the 69th minute as the twice European champions completed a 3-0 aggregate win.
Zenit, also leading 1-0 from the away leg, went ahead on the half hour when Venezuela forward Jose Rondon headed in Domenico Criscito's cross.
Hulk put his Brazilian World Cup misery behind him as he converted a penalty in the 54th minute following a trip on Igor Smolnikov.
Four minutes later, Hulk lived up to his name as he won possession in midfield, flicked the ball past one defender, held off another and burst his way past the third with the help of a lucky rebound before firing past Eiji Kawashima.
BATE, full name Borisov Automobile and Tractor Electronics, went ahead through Mikhail Gordeychuk four minutes before half-time and two late goals from Sergei Kryvets and Vitali Rodionov completed a 4-1 aggregate win.
Their Slovakian opponents had Seydouba Soumah sent off in the 79th minute.
Cypriot side APOEL, who reached the quarter-finals in 2011/12, outclassed Aalborg as they qualified for the group stage for a third time.
Vinicius, Tomas De Vincenti, Stathis Aloneftis and Cillian Sheridan shared the goals as they completed a 5-1 aggregate win over the Danes.
- Sports & Recreation
- Jackson Martinez
- Standard Liege