While Messi justified his status as the best player in the world with an injury-time solo goal that clinched Argentina's first win over its neighbor in six meetings, Spain conceded four goals for the second time since winning the World Cup.
Carlos Martins, an own-goal by Sergio Ramos, Helder Postiga and Hugo Almeida gave the home side victory in Lisbon.
Klaas-Jan Huntelaar gave World Cup runner-up the Netherlands a 1-0 win over Turkey, and France outclassed England 2-1 with a goal in each half at Wembley.
Italy's experimental lineup needed an 82nd-minute own-goal by Ciprian Marica to salvage a 1-1 draw against Romania in a match marred by racist taunts directed at Azzurri forward Mario Balotelli.
A youthful Germany team failed to unlock host Sweden as defenses dominated in a 0-0 draw, while the United States beat South Africa 1-0.
Argentina and Brazil looked to be heading for a scoreless draw in Doha, Qatar, after 90 minutes of a match more notable for the occasional rough challenge and bad-tempered reaction than the skills of Ronaldinho and Messi.
But the diminutive Argentine collected possession midway inside Brazil's half, beat four opponents and scored with a low shot into the right corner.
"Messi means everything to us," Argentina coach Sergio Batista. "He showed why he's the best player in the world." Spain eliminated Portugal in the second round of the World Cup in South Africa but was comprehensively beaten in Lisbon.
Martins opened the scoring in the 45th from a rebound after goalkeeper Iker Casillas had saved Cristiano Ronaldo's shot and Ramos poked Postiga's goal-bound shot into his own net three minutes after the break.
Joao Moutinho found Postiga for the third in the 68th before Hugo Almeida capped the Iberian derby victory in the third minute of injury time.
Spain's only wins in six matches since hoisting the World Cup have been in European Championship qualifying, against the weak trio of Liechtenstein, Lithuania and Scotland.
It has conceded 12 goals in its past four games.
Huntelaar scored in the 52nd for the Netherlands, but it was Hedwiges Maduro who set up the goal. The Valencia midfielder took the ball from Turkey left back Ismail Koybasi and crossed to Huntelaar, who knocked it in from close range.
The goal silenced a sizable Turkish crowd, which had been throwing flares onto the pitch throughout the game.
France put its humiliation at this year's World Cup further behind it with a fourth straight win and a fluent display, easing into a 2-0 lead at Wembley before injury-hit England got a late goal back.
Karim Benzema beat goalkeeper Ben Foster at the near post in the 16th and Mathieu Valbuena volleyed in from a cross by Bacary Sagna 10 minutes after halftime.
Peter Crouch came on as a substitute for the injured Steven Gerrard and volleyed in with his first touch direct from an 86th-minute corner.
"We didn't really pass the ball and we didn't really get going until the last 15 minutes," England captain Rio Ferdinand said. "We didn't play to our strengths today. We didn't control the ball and we didn't retain possession." Italy striker Balotelli, who was born in Italy but is of Ghanian descent, was jeered every time he touched the ball in neutral Austria - with the taunts coming from a group of about 100 extreme right-wing Italian fans at the match.
Stuttgart striker Marica put Romania ahead in the 34th with a shot from the edge of the area. He then scored at the other end following a corner from Andrea Pirlo.
Germany coach Joachim Loew fielded an experimental team with four players appearing for the national team for the first time. Defender Marcel Schmelzer and midfielder Lewis Holtby both started, while Andre Schurrle and Mario Goetze were introduced in the second half.
Scoring chances were scarce at either end. Germany's second-half substitute, Toni Kroos, came closest to breaking the deadlock but Swedish goalkeeper Andreas Isaksson clawed away his rising shot.
Sweden's best chance came when Ola Toivonen cleverly chested the ball in the penalty box, but Germany substitute Andreas Beck was on hand to prevent him getting a shot away.
Romelu Lukaku scored a goal in each half to give Belgium a 2-0 win over Russia, Egypt beat Australia 3-0 to hand Socceroos coach Holger Osieck his first loss since taking over in August, and Ghana dominated possession but was held 0-0 by Saudi Arabia.
In qualifying for the 2012 European Championship, Niko Kranjcar scored twice to lead Croatia to a 3-0 win over Malta that completed an unbeaten calendar year for the team for the first time since it started playing international football in 1991.
Croatia is top of Group F with 10 points, although second-place Greece is two points back having played one game fewer.
In the other qualifier, striker Mikael Forssell scored a second-half hat trick to help Finland to an 8-0 Group E win over tiny San Marino 8-0. Winless San Marino has now conceded 29 goals in five qualifiers.
The 40-year-old Jari Litmanen stretched his national record to 137 appearances as a second-half substitute, scoring the sixth goal from a 70th-minute penalty in what could be his last game for the national team.
"I cannot tell anything about how I will continue," Litmanen said. "In the near future, nothing will happen as there are not any games. I will look at what next year has to bring." Euro 2012 co-host Ukraine drew 2-2 against Switzerland.
World Cup-winning coach Marcello Lippi watched the game in Geneva, with speculation that the former Italy manager could be close to taking over the team.
Switzerland captain Alex Frei, a recent target for abuse by Swiss fans, scored twice to extend his national scoring record to 42 in what is likely his last home international.
Ukraine fought back through a deflection off Oleksandr Aliyev in the 48th, then Yvgenii Konoplianka's spectacular 75th-minute strike from distance.
Poland, the other co-host, ended an eight-game winless streak as Robert Lewandowski scored twice in a 3-1 win over Ivory Coast.
Roque Santa Cruz, who has made only two appearances for his club Manchester City this season, took advantage of some rare playing time to score two goals and set up two more in Paraguay's 7-0 thrashing of Hong Kong.
Santa Cruz opened the scoring in the fifth minute, heading in a pinpoint cross from the left wing, and Paraguay never looked back.
Seventeen-year-old substitute Juan Agudelo scored on his United States debut for a 1-0 win over South Africa in a friendly on Wednesday.
Agudelo, who turns 18 next Tuesday, exchanged passes in the 85th with fellow newcomer Mikkel Diskerud and scored with a shot that went in off the crossbar.
Serbia beat Bulgaria 1-0, Norway won 2-1 at Ireland and Israel beat Iceland 3-2 in other matches.
