With 18 minutes left, and the home side holding the one-goal advantage, Firmino came on for Sturridge.
Since then, Messi hasn't stopped against opponents from anywhere around Europe, with Arsenal being his major victim as he has scored nine times against the Gunners. However, Messi took the game by the scruff of the neck in the second half, delivering a reminder, as if one were needed, that this is a team that can put any opponent to the sword.More news: Hong Kong raises typhoon alert as Mangkhut approaches
Real Madrid have won the Champions League in each of the last three seasons.
Messi has also broken a tie with Cristiano Ronaldo to become the most prolific scorer of hat-tricks in the competition's history, with eight to his Portuguese rival's seven. Netted the second himself after a brilliant turn, curling home from distance to continue his goal-scoring form this season.
The win gets Liverpool off to a flying start ahead of their next match, an away trip to Napoli in early October.More news: Where does the Heat stand in the Jimmy Butler sweepstakes?
"Leo is the best in the world".
Messi led the way for Barca - who ended the match with 10 men following Samuel Umtiti's red card for a second bookable offence in the 79th minute. It was his eighth in Champions League play, the most ever, and it dispatched PSV Eindhoven in FC Barcelona's first UCL group-stage game. "Hopefully it's a year with a lot of titles".
"It was a bit lucky but I'll take it on my birthday", said Pulisic, who had missed two Bundesliga games for Dortmund and the USA friendlies against Brazil and Mexico.More news: Jurgen Klopp plays down seriousness of Firmino’s gruesome-looking eye injury
Barca were off the pace for much of the first half of Tuesday's Group B clash, but Messi broke the deadlock with a trademark free-kick. However, Atletico dominated for long spells and struck back before the interval through goals from Diego Costa and Jose Gimenez. Many supporters could not get to the games in MIlan or Barcelona in time after work and were forced to miss out because of these changes.