Celtic were 2-0 down from the first leg against Shakhter Karagandy, but an early goal from Kris Commons and two second-half strikes from Georgios Samaras and Anthony Stokes saw the Scottish champions through.
Also through are AC Milan, who produced a sterling performance to beat PSV Eindhoven 3-0 and 4-1 on aggregate. Kevin-Prince Boateng netted a brace before Mario Balotelli made sure of the win in the second half.
Real Sociedad piled more misery on Lyon, winning 2-0 in France to complete a 4-0 aggregate win. Former Arsenal man Carlos Vela scored twice in the second half for the Spanish side.
Zenit St Petersburg will also be in Thursday’s group stage draw after thumping Portuguese side Pacos Ferreira 4-2 on the night, and 8-3 on aggregate. Danny got a brace, while another former Arsenal man Andrey Arshavin also got on the scoresheet.
Stanislav Tecl scored as Viktoria Plzen won 1-0 at Maribor for a 4-1 aggregate victory.