The Argentina striker completed his treble in the 89th minute, shortly after substitute Jose Callejon had made it 3-0.
Champion Barca was 1-0 victors at bottom club Sporting where a 12th-minute strike from Adriano Correia was enough to earn it its first away success in the league this season.
Barca has 14 points from six games and is ahead of second-placed Levante on goal difference, after one of the season's surprise early form teams beat another, Real Betis, 1-0 away.
Juanlu's volley went into the net off the legs of Betis goalkeeper Casto Espinosa in the 33rd minute and from there on their rugged defense held firm to maintain their unbeaten start to the campaign.
The Valencia-based club, which claimed the scalp of Real two weeks ago, was one point ahead of Jose Mourinho's men in third, and Malaga and Valencia who both won on Saturday.
"I would like to have one more point, but one point is nothing really," Real coach Jose Mourinho told reporters. "The team that deserves all the attention (at the top) is Levante.
"They are the smallest, they don't get the same attention and they deserve it." Sevilla went sixth with 12 points, ahead of their city rivals Betis on goal difference, after a 0-0 draw at Atletico Madrid where goalkeepers Javi Varas and Thibaut Courtois both shone.
Real's lightning-quick counterattacks sank a spirited Espanyol in Barcelona with Cristiano Ronaldo laying on the first for Higuain after 17 minutes.
The Argentine, starting in place of the injured Karim Benzema, lashed his second into the far top corner in the 66th and Callejon sealed the win from Ronaldo's lay-off in the 82nd.
The youngster apologized to home fans who had idolized him over the previous three seasons before he returned to the Bernanbeu during the summer, and Higuain grabbed a late fourth.
"I had to work very hard to get back to playing again," Higuain told Spanish television, referring to the back injury that made him miss much of last season.
"I recovered as best I could and I'm now delighted to have had a game like this." Barca's Adriano scored after Xavi's shot came back off the post, but the visitors were not at their best and a third successive away draw was always a possibility in the face of a combative hosts.
"It was hard work but it was worth it," Adriano told reporters. "The points are worth their weight in gold." In the midday kickoff, Real Sociedad's Inigo Martinez scored from inside his own half in the Basque derby, but Fernando Llorente's brace made sure Athletic Bilbao earned a 2-1 away win.
Center back Martinez let fly from over 50 meters out and caught Gorka Iraizoz off his line, the visiting keeper perhaps distracted after one of his defenders had just been carried off on a stretcher.
Spain striker Llorente had put Bilbao ahead, turning in the area to score in the 34th minute, before Martinez levelled just past the hour mark in a sun-soaked San Sebastian.
Llorente then struck a superb volley to restore Bilbao's advantage in the 71st minute and earn under-pressure Argentine coach Marcelo Bielsa a first league win this season.
Bilbao climbed out of the bottom three to five points from six games, two behind their hosts in ninth.
