Australia held on to a narrow first-half lead to pick up a crucial victory over Tunisia that keeps alive their hopes of qualifying for the World Cup last 16.
Knowing defeat would mean an early exit from the competition, Graham Arnold's side came out of the blocks full of energy and intent.
Mitchell Duke took advantage of their positive start when he superbly flicked Craig Goodwin's cross into the far corner to put them 1-0 up after 23 minutes.
That sparked an outburst of jubilant celebration from the small contingent of Australia fans behind the goal, which momentarily silenced the hostile and unwavering support for Tunisia.
Hissed and jeered throughout by striking clusters of fans draped in red at the Al Janoub Stadium, Australia held their nerve to claim their first victory at a World Cup since 2010.
They survived a desperate onslaught from Tunisia in the second half, with Youssef Msakni forcing goalkeeper Mathew Ryan into a save at his near post, though that came moments after Mathew Leckie had come inches away from connecting with Goodwin's cross at the other end.
Stoke City defender Harry Souttar put in a superb performance, making several key blocks and tackles as Australia dug in.
Australia, who suffered a humbling defeat by France in their opening match, will take on tough opponents Denmark next - but with qualification in their own hands.
Significant victory for delighted Aussies
This was a crucial match for both nations given they face competition from defending world champions France and Euro 2020 semi-finalists Denmark to progress from Group D.
It could not have been a better start for Australia then, as they dominated the opening 15 minutes to leave Tunisia unable to get out of their half.
Goodwin's crosses from the left were initially dealt with, but the ease with which Australia were getting joy down that side will have caused concern for Tunisia.
Eventually, one of those crosses paid off as Duke expertly flicked Goodwin's delivery into the far corner and ran over to the touchline to receive a clamour of pats on the head from his team-mates.
That goal did little to silence the overwhelming majority of Tunisia fans in the Al Janoub Stadium, though, and it was their side who ended the first half stronger with two big opportunities to equalise.
Australia centre-back Souttar made a crucial, sliding block to deny Mohamed Drager, just minutes before Tunisia captain Msakni volleyed an effort inches wide.
Tunisia changed shape in the second half and put Australia under spells of relentless pressure. Aaron Mooy had to make another vital block, before Souttar yet again intervened to stop a dangerous counter-attack.
The anxiety was palpable in the stadium when Tunisia substitute Wahbi Khazri almost poked in a late equaliser, before six added minutes were signalled by the fourth official.
But Australia - who had to come through two play-offs to qualify for the tournament in Qatar - held on for a significant victory and they go into their final group match with all to play for.
Tunisia, who take on France in their final match, are all but out.
Player of the match
Squad number7Player nameMsakni
Squad number16Player nameDahmen
Squad number9Player nameJebali
Squad number23Player nameSliti
Squad number20Player nameDräger
Squad number3Player nameTalbi
Squad number4Player nameMeriah
Squad number24Player nameAbdi
Squad number11Player nameKhenissi
Squad number6Player nameBronn
Squad number10Player nameKhazri
Squad number14Player nameLaïdouni
Squad number17Player nameSkhiri
Squad number13Player nameSassi
Squad number21Player nameKechrida
Squad number13Player nameMooy
Squad number1Player nameRyan
Squad number15Player nameDuke
Squad number19Player nameSouttar
Squad number7Player nameLeckie
Squad number23Player nameGoodwin
Squad number16Player nameBehich
Squad number4Player nameRowles
Squad number22Player nameIrvine
Squad number14Player nameMcGree
Squad number5Player nameKaracic
Squad number9Player nameMaclaren
Squad number10Player nameHrustic
Squad number2Player nameDegenek
Squad number26Player nameBaccus
Squad number11Player nameMabil
9Jebali16Dahmen6BronnSubstituted forKechridaat 73'minutes4Meriah3Talbi20DrägerSubstituted forSassiat 45'minutesBooked at 90mins17Skhiri14LaïdouniBooked at 26minsSubstituted forKhazriat 67'minutes24AbdiBooked at 64mins23Sliti7Msakni9JebaliSubstituted forKhenissiat 73'minutes
Substitutes1Mathlouthi2Ifa5Ghandri8Mejbri10Khazri11Khenissi12Maâloul13Sassi15Ben Romdhane18Chaalali19Jaziri21Kechrida22Ben Saïd25Ben Slimane26Hassen
15Duke14McGree1Ryan5KaracicSubstituted forDegenekat 75'minutes19Souttar4Rowles16Behich7LeckieSubstituted forBaccusat 85'minutes22Irvine13Mooy23GoodwinSubstituted forMabilat 85'minutes15DukeSubstituted forMaclarenat 64'minutes14McGreeSubstituted forHrusticat 64'minutes
Match ends, Tunisia 0, Australia 1.
Second Half ends, Tunisia 0, Australia 1.
Ferjani Sassi (Tunisia) is shown the yellow card for hand ball.
Hand ball by Ferjani Sassi (Tunisia).
Attempt blocked. Wahbi Khazri (Tunisia) right footed shot from the left side of the box is blocked.
Foul by Taha Yassine Khenissi (Tunisia).
Milos Degenek (Australia) wins a free kick in the defensive half.
Foul by Montassar Talbi (Tunisia).
Milos Degenek (Australia) wins a free kick on the right wing.
Attempt saved. Wahbi Khazri (Tunisia) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by Wajdi Kechrida.
Attempt blocked. Naïm Sliti (Tunisia) left footed shot from the centre of the box is blocked. Assisted by Taha Yassine Khenissi.
Attempt blocked. Taha Yassine Khenissi (Tunisia) right footed shot from outside the box is blocked.
Substitution, Australia. Keanu Baccus replaces Mathew Leckie.
Substitution, Australia. Awer Mabil replaces Craig Goodwin.
Attempt saved. Montassar Talbi (Tunisia) right footed shot from outside the box is saved in the centre of the goal.
Foul by Ali Abdi (Tunisia).
Ajdin Hrustic (Australia) wins a free kick on the right wing.
Corner, Tunisia. Conceded by Harry Souttar.
Wahbi Khazri (Tunisia) wins a free kick on the left wing.
Foul by Jackson Irvine (Australia).
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