The former Borussia Dortmund face the strongest challenge in his career to prove his right to the money he has paid for 105 million euros, becoming the most expensive deal in Barcelona's history and the second most expensive deal in football history.
Ganso opened the scoring in the 46th minute before Wassim Ben Yedder doubled their lead in the 76th minute and Nolito sealed an eventually comfortable win in injury time.
The deflection put the ball into the path of Jordi Alba, who cut a pass back across the six-yard box for Messi to stab past Lopez.
The same two players combined again nearly immediately as Rakitic slalomed through the defence and played a sharp one-two with Messi before forcing a good low save from Lopez.
Barca made no such mistake as for all their early season off-field problems, Ernesto Valverde's men have taken maximum points from their opening three La Liga games. The No 10 appeared to be in for a quick-fire hat-trick, only to be denied by Marc Hermosa's last-ditch tackle.
Espanyol almost gave themselves hope when Pablo Piatti smashed a snapshot against the post, but that was a rare attacking foray and the second half started with Suarez - who was enduring a frustrating night - denied a close-range goal by Lopez's smart save.
Suarez was laid off by Deulofeu at Pau's near post not long afte the restart, but the goalkeeper kept out the striker's finish from point-blank range.
The Argentine was handed a slice of luck with his first goal, which should have been ruled out for offside, and then showed no mercy to Espanyol, moving on to five goals in three league games as record signing Ousmane Dembele came off the bench in the second half to make his Barca debut.
Real had one final chance to snatch a win when Kroos went for goal from the edge of the area but saw his shot bounce off the outside of the far post, leaving Zinedine Zidane's side with five points from their first three league games.
The opener arrived from the expected source but Messi should have been flagged offside before controlling Rakitic's immaculate pass, cleverly turning David Lopez and rifling into the top corner.
Five-time Ballon d'Or victor was in fine form, opening the scoring in the 26th minute, following up again ten minutes later, utilising expert service from Jordi Alba, sealing his hat-trick with more than 20 minutes remaining.
That proved to be the cue for Dembele's introduction, marked by the Barca fans chanting his name in unison.