Messi misjudged an opportunist lob with Hernandez stranded 18 yards out after misjudging Nicolas Otamendi's long ball but Venezuela threatened a leveller when a corner was not properly cleared, Rondon just unable to connect with a similar effort to Higuain's.
Arquimedes Figuera was ruled to have taken the ball rather than, as replays suggested, bundling Messi over in the penalty area and Wilker Angel blocked Higuain's shot.
Nicolas Gaitan's booking, for a hack at Alexander Gonzalez, ruled him out of a semi-final which moved a step closer when Figuera's woeful back-pass allowed Higuain to saunter around Hernandez and make it 2-0.
Figuera almost redeemed himself by setting up Rondon, who forced a superb reaction save from Sergio Romero, and the West Brom striker then headed against the left post from Seijas' corner.
Venezuela's resurgence continued as Romero had to adjust to tip Rolf Feltscher's deflected shot over before Martinez, having been denied one penalty, was awarded one after keeper Romero's clumsy challenge - but Seijas, a late inclusion in the line-up in place of the injured Adalberto Penaranda, was made to look foolish as Romero stood his ground to casually catch his chipped spot-kick.
Gaitan was just unable to put a hat-trick on a plate for Higuain straight from the second-half kick-off. Venezuela's Wilker Angel was then booked despite Figuera clearly being the guilty party as Messi was again fouled.
Messi put the game to bed on the hour after exchanging passes with Gaitan and finishing through Hernandez's legs.
Figuera was finally booked for his latest crude challenge on the Barcelona star, meaning he would have been dismissed but for the previous case of mistaken identity.
Rondon pulled a goal back with a header from Alejandro Guerra's left-wing cross but Argentina substitute Lamela immediately made it 4-1 with a deflected finish from Messi's pass.
And with little further goalmouth action it was Gerardo Martino's side who went forward to Tuesday's semi-final clash with the hosts in Houston.
In the other semi-final,
Chile thrashed Mexico 7-0 in Santa Clara to set up a last-four encounter with Colombia in Chicago on Wednesday.
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