Barca took some time to reach full flow in front of a far-from-full Camp Nou, but in Messi and Philippe Coutinho they always looked lively in the opposition half.
The hat trick was Messi's eighth in the Champions League, breaking a tie with Cristiano Ronaldo for the most in tournament history.
The 10 men got a fourth goal when Suarez picked out Messi, who guided the ball past goalkeeper Jeroen Zoet from 15 yards.
PSV Eindhoven were the visitors to the Camp Nou for the opening match in the 2018/19 edition and the Dutch champions were blown away by Messi's incredible individual display.
In the other Group B game played on Tuesday, Inter Milan scored two late goals, including a stoppage-time victor, to mark their return to the Champions League with a 2-1 comeback victory against Tottenham.
"I just want to be myself and win as much as I can here".
The other game in Group B saw Inter Milan come from behind to beat Tottenham 2-1 at the San Siro.
Dembele added to the lead with a well-placed shot from outside the area in the 75th, and Messi sealed the victory with goals in the 77th and 87th minutes.
He has now scored 104 goals in the competition and has netted in a 14th consecutive Champions League campaign - a joint record with Real Madrid legend Raul.