Former European Cup winners PSV Eindhoven were knocked out of the Champions League in the second qualifying round after a 2-1 defeat at Basel sent the Swiss side through on away goals on Tuesday.
Celtic, who won Europe's premier club competition in 1967, set up a clash with Romanians Cluj in the next stage after a 2-0 win at Nomme Kalju completed a 7-0 aggregate rout of the Estonian champions.
PSV won the first leg 3-2 but fell behind to a superb eighth-minute strike from Basel defender Eray Cumart, whose rocket of a shot from 20 metres cannoned in off the underside of the bar.
Bruma put PSV back in the driving seat when he levelled on the night with a thumping header from 15 metres midway through the first half, after a fine run by Donyell Malen.
The visitors missed several chances to seal the tie and were punished for their profligacy in the 68th minute when Basel's Dutch striker Ricky van Wolfswinkel swept the ball home from close range.
An Aleksandr Kulinits own goal gave Celtic an early lead before Ukrainian winger Marian Shved crowned his debut for the Scottish champions with a brilliant stoppage-time strike, having come on as a second-half substitute.
Celtic will face tougher opposition in Cluj, who ground out a 3-2 aggregate win over Maccabi Tel Aviv after a 2-2 draw in the return leg.
The Israeli side levelled the tie on aggregate after Nick Blackman gave them an early lead before goals from Juan Emmanuel Culio and Mario Rondon turned the tide.
Yonatan Cohen struck back for the home side shortly after the break but Cluj held on despite soaking up heavy pressure.
APOEL Nicosia breezed past Montenegrins Sutjeska Niksic with a 4-0 overall win after Serbian striker Andrija Pavlovic netted a hat-trick in his first start for the Cypriot champions.
Having come on as a late substitute in the first leg's 1-0 win on the Adriatic coast, Pavlovic, who is on loan at APOEL from Rapid Vienna, fired the home side into a 2-0 lead in the first half before adding the third in the 66th minute.
Olympiacos Piraeus, who were held to a 0-0 draw at Viktoria Plzen in the first leg, appeared to be struggling after a goalless first half in Greece but ran riot in the second as they celebrated a 4-0 win against the Czechs.
Dinamo Zagreb completed their 5-0 drubbing of Saburtalo after a 3-0 home defeat of the Georgians and will meet Ferencvaros in the next round after the Hungarian side knocked out Valletta 4-2 on aggregate.
Ferencvaros were skating on thin ice after Mario Fontanella converted a first-half penalty for Valletta but Tokmac Nguen struck back on the hour.