Messi scored Argentina's only goal of the tournament by converting from the spot but so far he has not come close to repeating the mesmeric performances he repeatedly delivers for Barcelona.
They will have to finish the stage as one of the two best teams to place third to stay on course for a first Copa America title since 1993.
The 31-year-old is desperate to win his first major trophy with Argentina and it's no exaggeration that he's having to do it all by himself at the moment.
"I feel that the team has the confidence to win this last group game", Messi said. "It will be a great step, even though we know they are also trying to advance to the next stage". "Shape is better but they still look like a team without a manager".
Perhaps two moments from Sunday's agonising victory sum up this Argentina first-round campaign to perfection. "It would be insane if we can't advance from the group stage, when basically three [teams] advance from each group".
Already-qualified Colombia lead Group B on six points after earlier beating Qatar 1-0, with Paraguay second on two points.
Argentina's caretaker coach Lionel Scaloni said his side had not played well and struggled to cope with the shock of conceding the first goal. "We're on the right track but we're still a long way from achieving all we really want", Rodriguez told reporters.
While Martinez tried gamely to keep his team moving forward, and Rodrigo De Paul promised on occasion with a handful of useful interventions, there was precious little support elsewhere on the pitch.
Not all of Argentina's problems lie with Scaloni, though, as he is the fourth coach to have taken charge since the 2014 World Cup and the national team set-up seems beset by short-termism.
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