Fenerbahçe, Legia Warszawa and Rosenborg secured narrow leads in their third qualifying round ties, while Celtic, København and Olympiacos all have work to do.
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Astana 1-1 Celtic
Yuri Logvinenko headed in Patrick Twumasi's corner to give Astana a 19th-minute lead, but Leigh Griffiths, who was also on the mark in the previous round, equalised with 12 minutes left after good work from Patrick Roberts.
Rosenborg 2-1 APOEL
Jørgen Skjelvik assisted Christian Gytkjaer for the Norwegian side's opener and then made it 2-0 himself with a high finish just prior to the break. Replacement George Efrem struck at the back post on 67 minutes to halve APOEL's arrears.
Astra Giurgiu 1-1 København
Debutants Astra went in front early on when Filipe Teixeira applied the finishing touch to Damien Boudjemaa's run and pass. København got an away goal midway through the second half, though, captain Thomas Delaney with a powerful shot from ten metres.
Trenčín 0-1 Legia Warszawa
Matúš Bero missed Trencín's best chance – Legia keeper Arkadiusz Malarz denied him from close range – and the visitors made them pay with 21 minutes left when Nemanja Nikolić turned in Michał Kucharczyk's low cross.
Olympiacos 0-0 Hapoel Beer-Sheva
The Greek title holders have work to do in Israel next week after both sides failed to find a breakthrough despite late chances.
Fenerbahçe 2-1 Monaco
The Istanbul giants have the upper hand courtesy of a goal in each half for Emmanuel Emenike, the second a superb volley from Gregory van der Wiel's cross. Radamel Falcao had drawn Monaco level on 42 minutes with his first strike since returning to the club.