Boštjan Cesar's header gave Slovenia hope of overturning a 2-0 play-off first-leg deficit, but Ukraine made it to UEFA EURO 2016, a red card and a late goal for the visitors twisting the knife for the home side.
The match in Maribor was played at full pelt from the off, with both captains booked in the opening exchanges. Yevhen Konoplyanka drew a save from Samir Handanovič but Slovenia seized the initiative, Cesar heading in at the far post after goalkeeper Andriy Pyatov had denied both Branko Ilić and Milivoje Novakovič from Valter Birsa's cross.
Ukraine were prevented from playing their usual game down the flanks but provided plenty of menace, Yevhen Seleznyov testing Handanovič with a volley. Slovenia kept up the pressure, though, yet for all the free-kicks they won, Birsa's deliveries never quite found their mark.
Handanovič kept his team in the running, making himself big to keep out Seleznyov's low drive after Konoplyanka had seized on Kevin Kampl's error. Nejc Pečnik had a chance to build on that moments before the break but shot straight at Pyatov after being played in on the left.
The pace did not dip after the interval, Handanovič fending off a Konoplyanka effort, but Ukraine's composure became more marked as time ticked on, Vyacheslav Shevchuk and Andriy Yarmolenko both getting attempts on target before Yaroslav Rakitskiy whipped one over the bar.
At the other end, Pyatov repelled another Cesar header following a Birsa corner in the last 20 minutes, and Zlatan Ljubijankič had a shot blocked in the box. Emotions boiled over as Mišo Brečko was sent off for a high challenge on Konoplyanka, and with Slovenia pushing desperately at the death, Ukraine countered, Yarmolenko finishing from Artem Kravets's ball. Game over.
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