Argentina, among the favourites to win the 2014 World Cup in Brazil, took over from Uruguay as the team to beat in the qualifying campaign.
Argentina ended a 39-year wait for another home win over the dogged Paraguayans in a World Cup qualifier and in securing it they sent their opponents to the bottom of the standings.
Messi might have had a third hat-trick in five internationals, hitting the woodwork twice, and his goal took his tally to 10 in six matches including friendlies.
"This is beautiful. It's lovely when the crowd give you so much love," Messi said.
Messi brought the best out of the players around him with Angel Di Maria and Gonzalo Higuain scoring fine goals. Sergio Aguero, seen as Messi's ideal partner in attack, was not even missed.
Argentina coach Alejandro Sabella, whose side stuttered at the start of the qualifiers, said: "We remain with our feet on the ground and we don't want the players to go from one extreme to the other ... Messi is happy and shows it on the pitch."
The nine-nation group without Brazil, who as hosts are spared the qualifiers, can be divided into two halves. The top four will go to the Brazil finals, the fifth team will have a 50-50 chance, playing off against an Asian side, and the bottom four will miss out.
Colombia, who had played below potential in a poor start to the campaign that included the sacking 10 months ago of coach Leonel Alvarez, climbed into the top five with a 4-0 rout of Uruguay in steamy Barranquilla.
"We mustn't lose focus of what this qualifying campaign is," Colombia's Argentine coach Jose Pekerman warned after the emphatic win sparked by red-hot striker Radamel Falcao's early opening goal.
"This was a key result against one of the best teams in the world ... (previously) 18 matches unbeaten, and we need to make the right reading of it," he said.
Colombia's win pushed Venezuela, who are looking to reach the finals for the first time but were beaten 2-1 away to Peru, down to sixth place.
Peru, who came from behind with a brace by reinstated, controversial winger Jefferson Farfan, climbed out of the basement now occupied jointly by Bolivia, who were beaten 1-0 by Ecuador, and Paraguay, quarter-finalists in South Africa two years ago.
The Peruvians will be looking to confirm their improvement when they host Argentina in Lima on Tuesday.
The same day, previous leaders Chile, who had a bye on Friday, entertain the Colombians, while Uruguay will be looking to pick up the pieces against Ecuador.
Uruguay coach Oscar Tabarez, who makes no bones about the qualifiers being tougher than the finals, saw his side drop to fourth two points behind Argentina and one short of Chile and Ecuador.
Ecuador, crushed 4-0 when they met Argentina in Buenos Aires in June, have quietly picked up a maximum 12 points from four home matches without conceding a goal, evidently taking advantage of the high altitude of Quito that handicaps their opponents.
Bolivia have been unable to do this, apart from a 3-1 home win over Paraguay in June due more to the ineptitude of the Paraguayans' former coach Francisco Arce, who was then sacked.
Experienced Uruguayan Gerardo Pelusso took over from Arce and had hoped to surprise Argentina with some tough defence and counter-attacking while admitting before the game no-one has succeeded in shackling Messi. His team were no exception.