The Uruguayan, who was on target in Barcelona’s European Cup final victory over Juventus, opened the scoring in California, before Sergi Roberto made sure of the win.
Tommy Meyer scored late in second-half injury time for defending MLS champions Galaxy, but it was a comfortable start to their treble defence from the Catalan giants.
In front of 93,226 fans – the biggest crowd for a club soccer game involving an MLS team in US history – Steven Gerrard’s second appearance in a Galaxy shirt never really got going.
Barcelona pressed relentlessly from the start in their first pre-season friendly in preparation for the defence of the La Liga, Copa Del Rey and Champions League trophies they won last season.
They were finally rewarded in the 45th minute when Suarez fired a left-footed shot past Galaxy keeper Brian Rowe after Rafinha’s deflected cross was moved on by Marc Bartra and Galaxy defender Leonardo was unable to clear the danger.
Both teams made wholesale changes at the break, with Suarez among the seven Barcelona players to depart and Andres Iniesta and Gerard Pique entering the game.
Galaxy coach Bruce Arena made five half-time substitutions, with Gerrard and Robbie Keane among those departing.
The changes didn’t slow Barca, with Douglas going close in the 47th minute and Pique testing substitute Galaxy keeper Andrew Wolverton in the 53rd after a pass from Munir.
Munir also helped set up Roberto’s 56th-minute strike from the edge of the box, which was clinically dispatched by the Spaniard.
The minority of Galaxy fans in the stands had little to cheer for much of the match, although Meyer grabbed a consolation goal in the first minute of injury time, heading in from close range.
Barcelona next travel up the coast to take on Manchester United on Saturday at Levi’s Stadium, home of the NFL’s San Francisco 49ers.