Last year's losing finalists Athletic Bilbao delivered an emphatic statement of intent as they hammered Finnish side HJK 6-0 at the Estadio San Mames.
Aritz Aduriz opened the scoring in the 25th minute and the tie was effectively over before half-time after further goals from Markel Susaeta and Inigo Perez.
Aduriz added his second six minutes into the second half before next week's second leg was rendered a formality by further strikes from Susaeta and Andoni Iraola.
Bilbao's Primera Liga rivals Levante also took a big step towards the group stages with a 2-0 win over 10-man Motherwell at Fir Park.
Juanlu opened the scoring for the visitors in the 42nd minute and Nabil El Zhar added a second in the 62nd minute before Motherwell defender Shaun Hutchinson was shown a straight red card.
Inter Milan had no problems seeing off Vaslui 2-0 in Romania, a goal in each half from Esteban Cambiasso and Rodrigo Palacio giving them a comfortable advantage ahead of the return in the San Siro.
And Serie A rivals Lazio are also heavy favourites to progress after goals from Hernanes and Miroslav Klose gave them a 2-0 win at Mura 05, who are still winless after six games of the new Slovenian season.
Hannover 96 had to bank on a pair of late goals from Leon Andreasen and Manuel Schmiedebach to emerge as the victors in an action-packed eight-goal thriller at Slask Wroclaw.
Andreasen and Jan Schlaudraff had put the Germans 2-0 up inside the first half-hour and despite Thomasz Jodlowiec reducing the deficit, Lars Stindl restored the two-goal advantage before half-time.
Wroclaw came out firing for the second half and drew level before the hour mark with gaols from Sylwester Patejuk and Przemsylaw Kazmierczak, before the two strikes in the last eight minutes finally swung the game Hannover's way.
PSV Eindhoven made up for a generally dismal night for their Dutch rivals as they thrashed Montenegro's Zeta 5-0 in Podgorica.
Ola Toivonen opened the scoring after two minutes but the Dutch giants had to wait until the 74th minute for the floodgates to open with further goals from Tim Matavz, Kevin Strootman, Jeremain Lens and Mark van Bommel.
Sporting Lisbon needed a late equaliser from Andre Carrillo to salvage a 1-1 draw with Horsens in Denmark, while Bordeaux take the momentum into the second leg after a goalless draw with Red Star in Belgrade.