But Marcelo Brozovic and Sammir dragged Zagreb back into it before half time and a 71st minute strike from substitute Fatos Beciraj drew them level on aggregate.
Steaua Bucharest blew an early two goal lead in Poland but clung on for a 2 2 draw on the night which gave them victory over Legia Warsaw on the away goals rule.
Schalke, Basel, Austria Vienna and Steaua Bucharest all reached the Champions League group stages on Tuesday night.
2 0 second leg win in Switzerland. Fabian Frei opened the scoring in the 11th minute and Philipp Degen added the second 11 minutes from time.
Leading 2 0 from the first leg in Croatia, the hosts extended their lead in the fourth minute through a Josip Simunovic own goal.
from Dinamo Zagreb to squeeze through to the James Harden Adidas New
Bundesliga side Schalke kept their nerve to edge past PAOK Salonika 3 2 in Greece for a 4 3 aggregate win.
Basle completed a 6 2 aggregate win over Bulgarian side Ludogorets with a Adidas High Tops Black And Blue
Vienna substitute Roman Kienast made a dramatic intervention to seal his side's place in the next stage, scoring their second just one minute after coming on as an 81st minute substitute, as a 3 2 defeat on the night gave the hosts a 4 3 aggregate win.
Adam Szalai's first half opener set the Germans on their way and despite a 53rd minute leveller from Stefanos Athanasiadis they regained control through Julian Draxler's 67th minute strike.
group stages at the Franz Horr Stadium.
A 79th minute effort from Kostas Katsouranis gave Salonika hope but Szalai's second in the final minute sealed victory for the visitors.
Austria Vienna survived a gallant fightback Adidas Harden Price
Nicolae Stanciu and Federico Piovaccari gave the Romanians a 2 0 lead inside the first 10 minutes before Miroslav Radovic pulled one back. Jakub Rzezniczak's injury time effort was too late for the hosts.
Austria Vienna Human Race Nmd Friends And Family For Sale and Steaua Bucharest all reach group stages
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