The Argentinian skipper was the architect of two Gonzalo Higuain strikes which came either side of an emphatic Messi penalty on the stroke of half-time at the Monumental Stadium.
The Barcelona superstar was Argentina's best player throughout, twice forcing Daniel Hernandez into scrambled saves early on before producing the pass which enabled Higuain to break the deadlock on 29 minutes.
Messi then harried Venezuela defender Gabriel Cichero into conceding a penalty, which the diminutive play-maker lashed into the roof of the net for 2-0 in first half stoppage time.
A trademark jinking run and through ball for Higuain gave Argentina their third in the 59th minute as Venezuela kissed goodbye to any chance of repeating their shock 1-0 win over the Argentinians in 2011.
The victory leaves Alejandro Sabella's side four points clear of second-placed Colombia at the top of the standings with 23 points after 10 matches.
With just six games remaining, only an unthinkable collapse will prevent the Albicelestes from taking their place at next year's finals in Brazil, with a trip to La Paz to face Bolivia on Tuesday their next game.
Los Cafeteros imperious
In other games, Colombia remained on course to end their 16-year World Cup exile after sweeping aside Bolivia 5-0 in Barranquilla.
Goals from Macnelly Torres, Carlos Valdez, Teofilo Gutierrez, Radamel Falcao and Pablo Armero secured an easy win as Colombia leapfrogged Ecuador into second place in the standings.
Colombia - who are revelling under the guidance of former Argentina coach Jose Pekerman - now look perfectly poised to reach their first FIFA World Cup since 1998.
Barranquilla's Metropolitano Stadium had rocked before kick-off as the home crowd paid an emotional tribute to former national keeper Miguel Calero, who died in December aged 41 after suffering a blood clot.
Colombia took the lead on 20 minutes, when Torres tucked away a cross from Juan Cuadrado, fortunate not to be ruled offside.
Colombia doubled their lead shortly after half-time when Bolivia failed to clear a knock-down from Abel Aguilar, which Valdez prodded home.
Gutierrez then made the game safe on 62 minutes, latching onto a through ball from Torres before steering past Bolivia's substitute keeper Sergio Galarza for 3-0. Falcao and Armero completed the rate late on.
Liverpool striker Luis Suarez looked to have settled a niggly encounter when he volleyed home a Nicolas Lodeiro cross on 82 minutes.
But Paraguay, who had rarely threatened during a stop-start game scarred by some rugged tackling, plucked an equaliser against the run of play four minutes later when substitute Edgar Benitez slotted home.
The first four finishers in South America's round-robin tournament will qualify automatically for Brazil, with the fifth-placed side facing a play-off against the fifth-placed side from Asia.