Barca got on the score sheet at home, when Messi curled home a stunning free-kick before the break.
Dembele lashed home Barcelona's second from long range in the 74th minute before Messi rounded off another dazzling display despite French defender Samuel Umtiti's late red card for two bookable offences.
The first goal of the 2018-19 Champions League group stage was a stunner from one of the all-time greats.
Barcelona coach Ernesto Valverde saluted the brilliance of Lionel Messi after the he scored his 48th career hat-trick. This is the Champions League and we're playing our first game against a team that's started well in their league, it was a hard game.
Substitute Roberto Firmino came to Liverpool's rescue after Paris St Germain hauled themselves back from two goals down in a five-goal thriller at Anfield.
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He'll continue to do this, as he has for a decade plus, and Barcelona will continue winning trophies - they project as the clear favorites to take La Liga, and a wide open Champions League is there for the taking. But Messi is a different player in the Champions League, a competition he has won four times, and in which he has scored 103 goals.
"He makes the extraordinary look routine".
The Dutch team is the 30th different club that the Argentine has scored against, since his debut goal against Panathinaikos in 2005. He has now scored in 14 different Champions League campaigns, with only Raul and Ryan Giggs ahead of him on 15 and 16 respectively.
FW Lionel Messi 9 - Some succulent early passes were not capitalised on by his teammates so the No.10 stepped up to the plate himself.
The 2018/19 Europe's elite club competition will kick-off on Tuesday, September 18 with the best European sides set to compete against each other in the tournament.