Argentina captain Messi struck a penalty in each half as the South American giants made sure of their place at next year’s finals in Brazil in emphatic fashion.
The Argentines — missing four of their first-choice XI through suspension — had only needed a point in the Paraguayan capital to be certain of qualification.
But Alejandro Sabella’s side demonstrated why they are likely to be regarded as one of the teams to beat in Brazil by tearing into the home team from the whistle.
Messi fired them ahead from the penalty spot on 12 minutes only for Paraguay to equalise through Jose Nunez six minutes later.
Manchester City striker Sergio Aguero restored Argentina’s lead on 32 minutes, shrugging off two markers before rifling past Roberto Fernandez to make it 2-1.
Real Madrid winger Angel Di Maria extended Argentina’s lead soon after half-time, sweeping forward on a lightning-fast counter attack and coolly steering a low shot beyond Fernandez on 50 minutes.
Argentina earned a second penalty moments later when Salustiano Candia was harshly adjudged to have fouled Messi in the area.
Messi duly dusted himself down and blasted in his second goal of the night to make it 4-1.
Paraguay veteran Roque Santa Cruz struck a late consolation goal for the 2010 World Cup quarter-finalists but Maxi Rodriguez hit back for Argentina in the dying minutes to make it 5-2.
Elsewhere Tuesday, second place Colombia missed their chance to clinch qualification after crashing 2-0 to Uruguay in Montevideo.
Late Uruguayan goals from Paris St Germain striker Edinson Cavani and Cristian Stuani handed the two-time World Cup winners a dramatic win at the Centenario Stadium as Colombia’s celebrations were put on ice.
The Colombians had needed only a point to be sure of clinching their first World Cup qualification since 1998 and for long periods looked more than capable of claiming the result they needed.
But Uruguay broke the deadlock 13 minutes from time.
A superb curling cross from Maxi Pereira was met by Cavani, who guided his header expertly past Colombian keeper David Ospina to make it 1-0.
Moments later Gaston Ramirez carved out some space inside the area and cut back to find Stuani who coolly tucked the ball away to make it 2-0.
It was a third consecutive victory for Uruguay which left them level on 22 points with fourth placed Ecuador, who drew 1-1 with Bolivia earlier Tuesday.
Colombia remain firmly on course to qualify however, requiring only a point from their final two fixtures to reach Brazil.
Uruguay (22 points) could still be mathematically overhauled by sixth placed Venezuela (19 points), who kept their faint hopes alive with a 3-2 win over Peru, but it would require an unlikely sequence of results for the Uruguayans to be denied either automatic qualification or a play-off place against Asian minnows Jordan.