Philippe Coutinho scored after just two minutes for Barcelona, who arrived in London winless in three La Liga matches, with Ivan Rakitic drilling in a magnificent second.
Messi, who had earlier twice hit the post then got on the scoresheet in between goals from Harry Kane and Erik Lamela, before Argentina superstar grabbed his second late on seal victory.
Barca head Group ‘B’ on six points alongside Inter Milan, but Mauricio Pochettino’s side face a vital double-header against PSV Eindhoven after failing to collect a point from their opening two matches.
Inter, the Champions League in 2010, again recovered from a goal down to beat PSV 2-1 in the Netherlands.
A cracking Pablo Rosario strike put PSV ahead, but Inter leveled through Radja Nainggolm moments after visiting goalkeeper Samir Handanovic somehow escaped a red card for handling outside his area.
PSG rebounded from their 3-2 defeat by Liverpool with an attacking masterclass against 1991 European Cup winners Red Star at the Parc des Princes.
Neymar curled in a sublime free-kick to open the scoring on 20 minutes, quickly doubling his tally before Edinson Cavani, Angel di Maria and Kylian Mbappe also found the target.
Former Germany international Marko Marin popped up with a consolation for Red Star, with Neymar completing his hat-trick from another stunning free-kick.
Tottenham Hotspur 2
(Kane 52, Lamela 66)
(Coutinho 2, Rakitic 28, Messi 56, 90)
Paris Saint-Germain 6
(Neymar 20, 22, 81, cavani 37, Di Maria 41, Mbappe 70)
Red Star Belgrade 1
Atletico Madrid (ESP) 3
(Griezmann 28, 67, koke 90+4)
Club Brugge 1
Borussia Dortmund 3
(Bruun Larsen 51, Alcacer 72,Reus 90+2)
PSV Eindhoven 1
( Rosario 27)
Inter Milan 2
(Nainggolan 44, Icardi 60)
Lokomotiv Moscow 0
( Mckennie 88)
FC Porto 1