Messi scored in the 60th minute to take his tally for the Albiceleste to 54 goals, matching the record held by Gabriel Batistuta.
The five-time World Player of the Year says: “I am happy to have equalled Batistuta’s record but my head is focused on lifting the Copa America.
“We are doing things right, we are growing and we need to keep down that same road.”
Argentina will now face the USA in the first semifinal tomorrow night in Houston.
Messi won the Man-of-the-Match award in an action-packed game against underdogs Venezuela, setting up goals for Gonzalo Higuain, who scored a brace, and Erik Lamela.
Reigning champions Chile joined them in the last four after a 7-0 demolition of Mexico in Santa Clara.
Hoffenheim striker Eduardo Vargas scored four goals to help them set up a semifinal date with Colombia on Wednesday.
Chile were unstoppable in the other quarterfinal in Santa Clara as they hammered a surprisingly fragile Mexico.
Edson Puch got his first and second international goals in the match.
Alexis Sanchez was involved in most of Chile’s great work and he made it 3-0 just three minutes into the second half, but Vargas was the star of the show with his four.