Shakhtar Donetsk began their Champions League campaign with a 2-0 win over Young Boys in the third qualifying round on Tuesday.
Bernard opened the scoring in the 27th minute, and the Swiss club's hopes of finding an own goal were dimed when Milan Vilotic was sent off with a second yellow card 10 minutes after half-time.
Yevhen Seleznyov added a goal in the 75th minute to give the Ukraine club a two-goal advantage ahead of the second leg.
BATE Borisov continued their quest to feature in the group stage for a second straight year with a 1-0 win at home over Irish champs Dundalk.
Substitute Mikhail Gordeichuk scored on 70 minutes, shortly after coming on, but the scoreline could have been worse as the Belarus side hit the woodwork twice.
Dinamo Zagreb, who also reached the group stage last year, won their home leg 2-0 over Dinamo Tbilisi thanks to goals from El-Arbi Hilal Soudani and Ante Coric shortly before half-time.
Dutch giants Ajax settled for a 1-1 draw at home with PAOK, Kasper Dolberg scoring for the hosts in the 58th minute after Djalma opened the scoring for the Greek side in the first half.
Russia's Rostov managed a draw in their Champions League debut, 2-2 at home against Anderlecht.
The Belgian side opened the scoring after just three minutes through Sofiane Hanni, but Saeid Ezzatollahi equalised for Rostov on 16 minutes.
Youri Tielemans again gave Anderlect the lead after the break, only for a Dmitry Poloz penalty on the hour mark to level matters again.
A Jonathan Soriano penalty was all Salzburg needed to grab a 1-0 win at Partizani, though both sides finished with 10 men as Diadie Samassekou and Reinaldo Kalari were both dismissed.
Following some fan trouble before the game, 1991 winners Red Star Belgrade earned a 2-2 draw at Ludogorets Razgrad.
After Jonathan Cafu gave the hosts the lead before the break, Aleksandar Katai and Guelor Kanga responded after half-time to put the visiors in front, before Claudiu Keseru scored Ludogorets' second.
Nicolae Stanciu scored a crucial own goal for Steaua Bucuresti at Sparta Prague in a 1-1 draw after Josef Sural's opener, while Viktoria Plzen and Qarabag played to a goalless draw in the Czech Republic.