Jon Dadi Bodvarsson swept Iceland into an 18th-minute lead at the Stade de France, with Austria paying dearly for Aleksandar Dragovic’s missed first-half penalty.

Substitute Alessandro Schopf levelled for Austria on the hour, but Traustason’s 94th-minute strike condemned Marcel Koller’s side to a premature exit.

Iceland, the smallest nation to appear at a major finals, will play England in the last 16 in Nice after finishing second in the group, behind Hungary but above Portugal, following a thrilling 3-3 draw in Lyon.

Iceland grabbed the crucial opening goal on 18 minutes as Aron Gunnarsson’s long throw was helped on into the path of Bodvarsson who steered past Robert Almer with Austria’s defence slow to react.

Centre-back Kari Arnason sliced narrowly over after a corner was only partially cleared, but Austria began to threaten with Arnautovic testing Halldorsson before heading over from a Julian Baumgartlinger cross.

And Marcel Koller’s side should have levelled on 37 minutes when Ari Skulason was penalised for tugging the shirt of David Alaba inside the area.

Dragovic stepped up but the centre-back fired the spot-kick against the outside of the post as Iceland breathed a huge sigh of relief.

Iceland still looked menacing though and Sigurdsson almost restored their lead on 65 minutes when his effort was rebuffed by Almer after a slick exchange of passes.

Schopf went close to firing Austria ahead after combining cleverly with Janko in the area, but Halldorsson blocked superbly with his legs.

Alaba’s dipping free-kick forced the Iceland keeper to turn over but Austria’s search for the crucial second goal saw them caught on the counter in the dying seconds as Traustason sealed a historic win.