Argentina were given a huge scare before ending Cape Verde's fairytale run as Lionel Messi netted his 20th World Cup goal in a 3-2 win after extra-time to reach the last 16.
Messi's sublime control and finish for his seventh goal at this tournament in four games put the defending champions in command, but the Blue Sharks doggedly refused to go away.
Deroy Duarte's strike on the hour mark forced Argentina to expand more energy than they would have wanted in the sapping Miami heat.
Lisandro Martinez briefly restored Argentina's lead early in extra time before Sidny Lopes Cabral's stunning shot rocketed into the top corner.
Another Argentina corner finally got the job done when Cristian Romero rose highest to head Messi's corner, the ball going in after taking a deflection off Diney Borges for an own goal.
La Albiceleste will face Egypt next on Tuesday in Atlanta, but there were concerns for Lionel Scaloni on his 100th match in charge despite what appears a favourable draw.
Cape Verde served warning of what they were capable of by holding European champions Spain, Uruguay and Saudi Arabia to draws in Group H to reach the knockout stages in their first World Cup appearance.
The Blue Sharks coach Bubista said the meeting with Messi and the world champions would be "the game of our lives" and it showed in a spirited display that had Argentina sweating for over 120 minutes.
On his return to the city where he now plays his club football for Inter Miami, Messi's every move was greeted like a god by the nearly 65,000 crowd that was awash of sky blue and white jerseys.
- Moments of magic -
The 39-year-old produced a moment of magic with a feather-like touch from Lisandro Martinez's pass to set up a high finish past Vozinha to open the scoring.
In doing so Messi also extended his own record of scoring in eight consecutive World Cup games and opened up a two-goal cushion once more over France's Kylian Mbappe in the battle to be the competition's all-time top goalscorer.
Emi Martinez had been a spectator in the first half, but the Aston Villa goalkeeper was forced into a smart save by Duarte as Cape Verde started the second period with more attacking intent.
Martinez was powerless for the equaliser moments later when Duarte was picked out by Ryan Mendes and rifled a low shot into the far corner.
Cape Verde's 40-year-old goalkeeper Vozinha became an internet sensation after his man-of-the-match showing against Spain last month.
His nearly 18 million Instagram followers will have enjoyed him winning a one-on-one battle with Messi when the eight-time Ballon d'Or winner seemed certain to restore Argentina's lead.
Irish-born Pico Lopes was next to be a Cape Verdean hero with a crucial intervention to deny Enzo Fernandez a tap-in after more inspiration from Messi created an opening.
Lisandro Martinez's rising drive after a corner fell the Manchester United defender's way two minutes into extra-time looked to have swung the momentum decisively in Argentina's favour once more.
But again Cape Verde refused to bow and levelled with one of the goals of the tournament when Lopes Cabral smashed into the top corner.
The full-back ran off into the stands to celebrate with his partner.
Elsewhere around the crowd, the boisterous atmosphere that had accompanied most of the evening gave way to nervous tension as penalties approached.
Scaloni could only wipe his furrowed brow with relief when Messi's corner was turned in for an own goal by the unfortunate Borges.
Yet an exhausted Argentina still had to ride their luck from a Cape Verde onslaught in the final seconds.
Emi Martinez this time won the battle with Lopes Cabral by tipping over another sweet strike that was headed for the top corner.
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