The World Player of the Year combined brilliantly with Sergio Aguero to give his side a 19th-minute lead in their first friendly in Europe under coach Alejandro Sabella.
Xherdan Shaqiri equalised for the Swiss early in the second half but Messi struck again in the 87th minute after a blunder by the home defence and then completed his first international hat-trick with a last-minute penalty.
Even Switzerland's usually dour coach Ottmar Hitzfeld managed a smile when asked about Messi's performance.
"It was emotional to watch him, his speed and explosiveness are astonishing. He has showed again he is the best in the world," the German told reporters.
Sabella, who replaced Sergio Batista following the Copa America in July, said he never doubted Messi who has already scored 43 goals for Barcelona in all competitions this season.
"It's a blessing for us to have Messi in the team," he said before praising his team-mates for working hard to provide the playmaker with the ball.
Earlier, Argentina struggled on a difficult pitch against some rough Swiss tackling in a Stade de Suisse eerily quiet despite a capacity 30,000 crowd.
One Argentine drum was beaten incessantly and the odd cowbell was heard while Argentine radio commentators with rapid-fire deliveries could be made out several rows away.
A bizarre half-time competition on the pitch involving the throwing of giant dice appeared to entertain the fans more than the match.
TACTICAL FOULS
Messi had already had a couple of runs at the Swiss rearguard before his opening goal came when played the ball to Aguero who backheeled a return for his colleague to slot the ball into the bottom corner.
Soon after Messi dribbled round the entire defence and pulled the ball back into the penalty area but his team-mates failed to read the move.
The visitors enjoyed long periods of possession but were repeatedly halted by tactical fouls in the Swiss midfield which went unpunished by the referee including two clear yellow card offences by captain Gokhan Inler.
Rodrigo Brana, who was repeatedly kicked, had to be substituted at half-time with a knee injury.
Switzerland fielded a young side including four members of the team that finished second in last year's European Under-21 Championships.
They equalised five minutes after the break when Shaqiri fired into the roof of the net.
The move came immediately after an Argentine break where Aguero burst clear of the last man and appeared to be tripped only for the referee to wave play on.
Argentina had their worst spell of the match after the Swiss goal as the service to Messi temporarily dried up, the team's main failing under Sabella's predecessor Batista.
A draw appeared on the cards until Swiss defender Francois Affolter lost possession to Aguero on the edge of the box with three minutes left.
Aguero fed
