Austria scored a 96th-minute equaliser to save themselves from elimination, while taking them and Algeria through to the knockout stages.
It was a straight shootout for second place behind Argentina in Group J, and the two sides played out a six-goal thriller at Kansas City Stadium.
Marko Arnautovic latched onto David Alaba’s long ball and broke the deadlock in the 28th minute, but Rafik Belghali’s superb individual goal levelled things up at half-time.
Marcel Sabitzer’s superb first-time finish from a Konrad Laimer cross restored Austria’s lead, but they found themselves on the brink of elimination after Riyad Mahrez completed a brace in stoppage time.
However, there was time for one more dramatic twist, as Michael Gregoritsch kept a deep cross alive for Sasa Kalajdzic to head in the equaliser and take both sides through.
Algeria vs Austria analysis:
Algeria almost banish the ghost of Gijon
When the two sides were drawn together in Group J, memories of 1982 came racing to the surface.
It was then that Austria denied Algeria progress from their group, after playing out a mutually beneficial 1-0 defeat against West Germany in what was dubbed “the Disgrace of Gijon”.
That is the reason why all final group games are now played simultaneously.
Ironically, after twice coming from behind to level at 2-2, Algeria took their foot off the gas and slowed the momentum of the game right down, knowing defeat would see them eliminated.
However, they suddenly sprung into life to catch Austria off-guard in the 93rd minute, as Houssem Aouar slipped in Mahrez to make it 3-2.
Set to be heading for the exit at that point, Ralf Rangnick swiftly threw on six-foot-seven Kalajdzic, and the move was instantly justified as the giant striker headed in to rescue his side at the death.
Following a hugely entertaining 90 minutes, both sides take their places in the round of 32.
Golden oldies shine in six-goal thriller
Two of the most telling contributions in this epic clash came from players well-known to Premier League fans.
Former Stoke and West Ham forward Arnautovic, at 37 years and 70 days, became the oldest Austrian to start a World Cup match, and marked the occasion with a well-taken finish to break the deadlock.
The first Austria player to score multiple goals at the World Cup and European Championship, he also joined an exclusive group of players who have netted two or more times in this competition when aged 37 or older. The others are Lionel Messi, Cristiano Ronaldo and Roger Milla.
Arnautovic was withdrawn at half-time, and from the hour mark onwards, it was former Leicester and Manchester City winger Mahrez who took centre stage.
The 35-year-old’s pair of neat finishes made him the first Algeria player aged 32 or older to score a goal at the finals, and he will hope to inspire them further during only their second venture into the knockout rounds.
The late, late show rescues Austria
Austria are through to the knockout stages at the World Cup for the first time since 1954, though they progress while breathing a huge sigh of relief.
With the advantage over Algeria via goal difference, a draw was always going to be enough to secure second place in Group J. Although, the fact it stood at zero meant any slip-up would see them drop out of the top eight best third-placed teams.
Even though they were twice pegged back – and had just 34.9% of possession overall – Rangnick’s side appeared in control of things, and the greater degree of concern appeared to lie with their opponents.
Out of nowhere, though, Austria were staring down the barrel of elimination after Mahrez’s stoppage-time strike.
Yet Rangnick’s instinctive decision to send on Kalajdzic paid dividends just 61 seconds later, as Austria became the first team to avoid defeat in a World Cup match after conceding a go-ahead goal in the 90th minute or later.
They got away it this time, but it was a stern warning that they probably won’t against much-fancied Spain in the round of 32.
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