Argentina had its chances against Paraguay in Asuncion, but the Copa America champions could not find the breakthrough on Thursday.
Lionel Scaloni's Argentina, though, remain unbeaten in second position after nine matchdays on the road to Qatar 2022 and undefeated across 23 games across all competitions.
Messi was entering the contest on the back of his record-breaking exploits during the last international break after surpassing Brazil great Pele (77) as the all-time leading scorer for a South American nation with his hat-trick against Bolivia.
The Paris Saint-Germain superstar looked lively away to Paraguay, creating a great opportunity for Argentina to break the deadlock in the 11th minute.
Messi, who had received 437 passes in CONMEBOL qualifying – the most by any player in the campaign – weaved his way past defenders and slid a ball through to a team-mate, whose goal-bound effort was somehow cleared off the line by a scrambling Omar Alderete ahead of Angel Di Maria.
Argentina was largely in control in the opening half, though Paraguay had some moments in the attacking third.
Another chance went begging for Argentina within five minutes of the second half getting underway, Rodrigo de Paul's ball across the six-yard box somehow evading his team-mates.
Paraguay almost took a surprise lead four minutes later after Miguel Almiron's turn of pace created an opening, but Emiliano Martinez was up to the task to deny the Newcastle United star.
Di Maria picked out Joaquin Correa at the back post on the hour mark, however, some desperate defending blocked the Argentina forward's goal-bound header.
Martinez was kept rather busy in the second half, but the in-form goalkeeper continued to thwart Paraguay, who were searching for their first home World Cup qualifying win against Argentina since 2009.
Antony Silva produced a fabulous sequence to deny Argentina during the closing stages, first dealing with Guido Rodriguez's header before pushing Papu Gomez's long-range effort onto the crossbar seven minutes from the end, while Carlos Gonzalez almost snatched victory for Paraguay in the 88th minute.
What does it mean? Unbeaten run continues
While Argentina were unable to secure maximum points, the South American champions have not tasted defeat since 2019.
Goalkeepers flex muscles
It was a showdown between two goalkeepers at the top of their game. Martinez came up big for Argentina in the second half, while Paraguay counterpart Silva was not to be overshadowed in a strong display.
Paraguay struggling for home form
While Paraguay would have probably taken a point before the match, their home woes continue. Paraguay have only won one of their past eight World Cup qualifiers on home soil, dating back to March 2017.
Argentina are back in action for the visit of Uruguay on Sunday, while Paraguay are away to Chile on the same day.