The Spanish champions' all-time top scorer Messi broke the deadlock in the 32nd minute with an immaculate free kick which he curled over the wall into the top corner against a PSV side who had defended well and looked dangerous on the break.
But Barca demonstrated the gulf in class as the second half progressed and doubled their lead in the 75th with a curling strike from French forward Ousmane Dembele, who scored his fifth goal in six games in all competitions this season.
Messi got his second two minutes later when he turned Ivan Rakitic's dinked pass into the net with a flick of his boot.
The mood was briefly dampened when Barca's France defender Umtiti was dismissed in the 79th for a second yellow card before Messi completed his treble three minutes from time.
The Argentine received another chipped pass, this time from Luis Suarez, and ruthlessly smashed the ball home.
The strike completed eight trebles in Europe's top competition for Messi, one more than rival Cristiano Ronaldo who will make his Juventus Champions League debut on Wednesday.
EXTRAORDINARY MESSI
"Messi does extraordinary things and makes them look routine," Barca coach Ernesto Valverde told reporters.
"We have to pinch ourselves to remind us that we are living through a unique era. When he stops playing it will be difficult to find someone like him."
PSV, coached by former Barca and Netherlands midfielder Mark van Bommel, had produced an admirable performance on their first visit to the Nou Camp in 21 years until they tired late on.
In the first half they shut down most of Barca's attacks and plotted several spirited breaks, while after the interval their Mexico international Hirving Lozano fired just over the bar.
Van Bommel thought his side were hard done by in conceding the free kick from which Messi opened the scoring but he also paid tribute to the five-times world player of the year.
"I don't think it was a foul but Messi put it in the net. For me he's the best player in the world and it's strange to me he doesn't win the Ballon d'Or every single year. But, overall, I think the scoreline was harsh on us."
Barca lead Group B on goal difference after Inter Milan beat Tottenham Hotspur 2-1 at the San Siro. Umtiti's dismissal rules him out of Barca's next game at Spurs Hotspur on Oct. 3.
(Reporting by Richard Martin; Editing by Toby Davis and Ken Ferris)
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