Basle led for 75 minutes of their Europa League tie , but failed to add the crucial second goal before McGeady’s 90th-minute equaliser won the tie outright for the hosts.
Having been beaten 3-2 at home in the first tie, Basle needed to win by two clear goals and things started well when Scott Chipperfield netted after 15 minutes.
The Swiss side could not fashion a second though, meaning their Russian opponents would have progressed on away goals before McGeady secured a 4-3 aggregate victory anyway in the closing moments.
After a couple of near misses the leveller came just into added time, Dzjuba playing in McGeady to slot home from six yards.
Maurice Edu scored a dramatic last-gasp goal to send Rangers into the last 16, after a 2-2 draw was enough to see them through on aggregate against Sporting Lisbon.
El-Hadji Diouf claimed his first goal for Rangers before strikes from former Rangers midfielder Pedro Mendes and Yannick Djalo appeared to have secured victory for the home side at the Jose Alvalade Stadium. But Edu pounced in injury time with the decisive goal in the tie as Rangers triumphed on away goals after the first leg had ended 1-1.
Roman Shirokov’s late strike capped a dramatic comeback by Russian champions Zenit St Petersburg as the 2008 UEFA Cup winners hit back from a 3-1 aggregate deficit to defeat Young Boys.
Taking a 2-1 first leg advantage to the freezing Russian city, the Swiss side took even tighter control when Ammar Jemal headed the opener from close range with 21 minutes gone.
But shortly before the break Danko Lazovic equalised on the night and Zenit were level on aggregate in the 52nd minute when Sergei Semak fired home. Shirokov’s left-footed winner came 13 minutes from time.
Goals from Nilmar and Giuseppe Rossi saw Villarreal past Napoli 2-1 on aggregate after a goalless first leg while Benfica won 2-0 at Stuttgart to progress 4-1 on aggregate.
FC Twente weathered an early storm from Rubin Kazan to seal their place with a 2-2 draw at the Arke Stadion, having claimed a 2-0 win in the first leg in Russia.
Second half goals from Balazs Dzsudzsak, Jeremain Lens and Marcelo earned PSV a 3-1 win over Lille for a 5-3 aggregate win, while Michael Ballack scored as Bayer Leverkusen wrapped up a 6-0 aggregate rout of Metalist with a 2-0 win in Germany.
Ajax cruised past Anderlecht 5-0 on aggregate after a 2-0 win in Amsterdam while Dynamo Kiev demolished Besiktas 4-0 for an 8-1 aggregate win.