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 Wednesday in Atlanta, but there were concerns for manager Lionel Scaloni during 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 more than 120 minutes.
On his return to the city where he 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 with sky blue and white jerseys.
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 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.
Emi 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.
Deroy Duarte celebrates his goal against Argentina. Photo / AFP
But again Cape Verde refused to bow and levelled with one of the goals of the tournament when Lopes Cabral smashed the ball into the top corner.
The fullback 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 heading in.
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