Leonardo Mayer beat Joao Souza 7-6(4), 7-6(5), 5-7, 5-7, 15-13 in a Davis Cup singles match that lasted a record six hours and 42 minutes to haul Argentina level with Brazil at 2-2 in their first-round tie on Sunday.
Argentine Federico Delbonis led Thomaz Bellucci after taking the first set of the final rubber 6-3 when play was suspended for poor light. The pair will resume on Monday looking to put their country into a quarter-final against Serbia.
Mayer won on his 11th match point in a battle of the South American rivals' number ones in searing heat on a purpose-built clay court at the Tecnopolis exhibition complex on the outskirts of the capital.
The match lasted 20 minutes longer than a clash in 1982 when John McEnroe beat Mats Wilander in a United States v Sweden quarter-final in St Louis.
The longest Davis Cup match was a 2013 first round doubles tie in Geneva in which Czechs Tomas Berdych and Lukas Rosol beat Marco Chiudinelli and Stanislas Wawrinka of Switzerland 6-4, 5-7,6-4, 6-7(3), 24-22 after seven hours and one minute.
Mayer looked like he might be on his way to a three-set victory when he led 4-1 in the third but Souza recovered, making the most of two double faults by his opponent to take the set, and then won the next to level the match.
Mayer had three match points at 5-4, two at 9-8, three at 12-11, another at 13-12 and finally two more, an unreachable return on the 11th finally ending Souza’s resistance in the Brazilian’s second five-set marathon in three days.
Mayer fell to the clay court after sealing the win, but quickly rose and began jumping around with delight and cried with relief.
He later needed medical attention for exhaustion.
Switzerland's Davis Cup reign ends swiftly
Switzerland's reign as Davis Cup holders was swiftly ended when they paid the inevitable price for fielding a second-string team and lost 3-2 to Belgium in the first round in Liege on Sunday.
Just over three months since Roger Federer and Stanislas Wawrinka drove them to an historic title in Lille, it was a different story without their big two as the Swiss became the first champions in 10 years to fall at the first hurdle.
Federer and Wawrinka had chosen to stand aside after achieving their ambitions and the stand-ins were not able to upset the odds against much higher-ranked players despite a heroic effort from 22-year-old Henri Laaksonen.
The world number 344, who previously played for Finland, levelled the tie at 2-2 with a 6-3, 3-6, 3-6, 7-6 (5), 6-1 win over Steve Darcis, a player ranked 242 places higher.
For the second time in three days, the remarkable Laaksonen fought back to prevail in a five-setter.
Switzerland's hopes, though, were extinguished in the deciding rubber when David Goffin, the world number 21 who was rested on Friday because of concerns over a back injury, proved too good for number 321 Adrien Bossel and won 6-4, 6-0, 6-4.
For the second year running Andy Murray led Britain to a first-round victory over the United States when he beat John Isner 7-6 (4), 6-3, 7-6 (4) in Glasgow.
The former Wimbledon champion survived some early scares against the big-serving American before taking charge to steer Britain into an unassailable 3-1 lead.
In the quarter-finals they face a home tie against France who beat Germany with a day to spare.
Italy, who beat Britain in the quarter-finals last year, went down to Kazakhstan in Astana where Aleksandr Nedovyesov, ranked 130th in the world, stunned number 22 Fabio Fognini in five sets to seal a 3-2 victory.
Kazakhstan next travel to former Davis Cup heavyweights Australia who enjoyed a 3-1 victory over 2012 and 2013 winners Czech Republic in Ostrava, Bernard Tomic clinching the win with a 7-6 (4) 6-3 7-6 (5) triumph over Lukas Rosol.
Australia are through to the last eight for the first time since 2006.