Austria Vienna and Steaua Bucharest have both booked their place in the Champions League proper, while Basel will also be in the pot for Thursday's draw.
The Croats, who went into the conclusion of the tie losing 2-0 on away goals following Wednesday's first leg, were given a seemingly insurmountable task in their quest to reach the Champions League proper after Florian Mader fired his side in front after only four minutes.
However, two goals Marcelo Brozovic and Junior Fernández gave Zagreb a fighting chance going into the second half, before Fatos Beqiraj struck 20 minutes from time to put his side ahead in the tie. Kineast pounced four minutes from time to seal his team's progression on a 4-3 aggregate, though.
Elsewhere in Europe, Steaua Bucharest also put its name in the pot for Thursday's draw in Monaco courtesy of an away-goals victory over Legia Warsaw after they played to a 3-3 aggregate draw.
The Romanians went into the second leg trailing on away goals after last week's 1-1 draw, but the advantage was soon wiped out courtesy of two quick-fire goals from Nicolae Stanciu and Federico Piovaccari.
Miroslav Radovic halved the deficit soon after, before Rzezniczak struck in stoppage time but it was not enough for the Poles to earn their place in the Champions League proper for the first time since 1995-96.
Meanwhile, Basel coasted into the group stage of Europe's elite competition following a 6-2 aggregate victory over PFC Ludogorets Razgrad, with Fabian Frei and Philipp Degen netting either side of halftime to ensure progression over the Bulgarian outfit.