Needing a point to advance from Group F, the tournament debutants once again showed their iron will in defence - that had notably thwarted Cristiano Ronaldo and Portugal in the opening week - to keep out a swarming Austrian front line.
Austria had their chances, but Aleksandar Dragovic's first-half penalty miss, after Jon Bodvarsson had put Iceland ahead, will be looked back on ruefully.
Alessandro Schopf equalised after the interval and Austria spent much of the second half camped in opposition territory, but stout defence and Traustason's counter-attacking effort gave the travelling hordes from Iceland a moment to savour.
Austria, who were backed to make a strong showing at Euro 2016, exit the competition after picking up one point from their three group games, in which stars like David Alaba and Marko Arnautovic struggled to make an impact.
Iceland are unbeaten in the competition and have only lost one of their last nine competitive matches in a run of form that leaves England with no room for complacency as they meet a team who are entering unchartered territory under the guidance of Lars Lagerback and Heimir Hallgrimsson.
Perhaps expected to sit back from the off, Iceland signalled their intent when a 25-yard rocket from Johann Gudmundsson rattled the left-hand post in just the second minute, and Austria struggled to settle into the game as their opponents dictated the pace.
A momentary lapse from Hannes Halldorsson almost allowed Marko Arnautovic to dispossess him in the six-yard box, but a desperate challenge from the goalkeeper denied the Stoke City striker.
Austria were made to rue the missed opportunity after 19 minutes, when Aron Gunnarsson's long throw-in was flicked on by Kari Arnason to Bodvarsson, who turned neatly and fired the ball into the far corner of the net.
As Austria pressed for an equaliser, Ari Skulason fouled Alaba in the penalty area but Dragovic's spot-kick clipped the outside of the post, and Iceland had the ball in the net just a minute later, through Birkir Bjarnason was flagged offside.
Austria had a claim for a second penalty turned down when Marcel Sabitzer was bundled over by Skulason, and Arnason had to fling himself in the way of a Sabitzer half-volley minutes later to keep the scores level.
Halldorsson saved from Schopf's thumping shot from the edge of the penalty area, but the substitute made no mistake moments later when he waltzed through Iceland's defence and buried his shot into the corner of the net.
Schopf and Alaba forced further saves out of Halldorsson as Austria's attempts began to grow desperate.
Almer went up for a corner as Austria rolled the dice in injury time, but Elmar Bjarnarson broke up the other end and squared to Traustason, who converted at the far post to send Iceland into dreamland.