Dembele, who had been rampant throughout, scored Barcelona's second by completing a slick run through PSV's back line with an even better finish and Messi added his team's third with a cool first-time shot from an Ivan Rakitic pass over the top of the visitor's defence.
In the first period they successfully shut down most of Barca's attacks and also plotted several unsafe breaks, which led to Mexico worldwide Hirving Lozano firing narrowly over the bar after the interval.
The 25-year-old has been recently linked with a move to the Camp Nou after helping France win their second ever World Cup title in Russian Federation in July.More news: Senators fight over witnesses for Kavanaugh hearing, accuser might not show
'My agents told me that Barca asked about me and it would be a dream to play here in the future, but now the important thing is focusing on PSV and enjoying it as much as possible'.
"It would be a dream come true to come to this great club".
Lozano was one of Mexico's better performers over the summer and continues to shine for his club side as well.
"If tomorrow we get a good result, I don't care if they fight for Messi's shirt", Van Bommel told a news conference on Monday. "I always want to play to help, but I couldn't last season". The Catalans and their players including Leo Messi and Luis Suarez have highlighted their hunger to win the Champions League after watching arch rivals Real Madrid lift the prestigious accolade on three consecutive occasions.