A pair of own goals either side of half-time put Ernesto Valverde's side comfortably ahead before Suarez marked his milestone by wrapping up the three points.
Girona skipper Aday Benitez was the victim for the opener when he deflected Jordi Alba's strike into his own net to gift the league leaders an early advantage.
And it was another own goal which doubled Barca's lead after the interval as Aleix Vidal's classy cut-back wriggled in off Girona goalkeeper Gorka Iraizoz.
Suarez added the gloss with 20 minutes remaining to seal a sixth consecutive league victory, an impressive start they last managed in 2013-14.
While far from perfect at the back, Valverde's men now sit four points clear of second-placed Atletico Madrid.
The visitors had early joy down the right when Javier Mascherano found Vidal in behind, but the winger's attempted cross was crucially cut out by Iraizoz.
Marc-Andre ter Stegen next produced a superb one-handed save low to his right to deny Douglas, while Suarez's inability to find a team-mate from a cut-back at the other end cost Barca a certain opener.
Valverde's side did not have to wait long for the breakthrough, though, and it came courtesy of a huge slice of fortune.
After Iraizoz kept out Messi's free-kick, the veteran keeper was left with no chance from the resultant corner as Alba's speculative volley took a heavy deflection off Benitez on its way into the bottom-left corner.
Barca began to take control by the half-hour mark and only an in-form Iraizoz prevented them from doubling their advantage, the 36-year-old quick off his line to smother another chance for Alba.
Paulinho and Michael Olunga still found time to exchange wayward headers as an entertaining first half ended with the away side ahead.
The lead became 2-0 almost immediately after the resumption when Vidal reached the by-line and attempted to find Suarez, who hurdled the back-heel pass and saw it trickle in via Iraizoz's legs.
Girona continued to pose a threat in the air with Douglas heading another opportunity high, while Olunga nodded straight at Ter Stegen just before the hour.
But any hint of a comeback was soon extinguished thanks to Suarez. The striker was put clean through by Sergi Roberto and clinically picked out the bottom-left corner to make it 3-0.
With their perfect league record still intact, Barca will take plenty of confidence into their midweek Champions League trip to Sporting CP.
