The Spanish teenager was back in action after hand and back problems forced him to pull out of last week's 2023 debut on European clay at the Monte Carlo Masters.
The top seed swept aside the world number 79 from Portugal 6-3, 6-1 to set up an all Spanish last-16 clash with Roberto Bautista Agut after the 13th seed beat Bernabe Zapata Miralles 6-2, 6-2.
"I feel great," said Alcaraz, playing on the surface for the first time since Rio de Janeiro in February.
Alcaraz pulled out of Monte Carlo with the injuries that had hampered his last appearance, in the semi-finals in Miami where he succumbed to Jannik Sinner.
Alcaraz arrived in Miami as the world number one after success at Indian Wells, but was knocked off the top of the ATP rankings by Novak Djokovic after the loss to Sinner.
The 19-year-old's bid to successfully defend a tour-level title for the first time got off to the best possible start, as he despatched Borges in 63 minutes on the court named after Rafael Nadal, another absentee from Monte Carlo.
Aside from unforced errors that enabled Borges to reclaim a break in the eighth game, Alcaraz showed little sign of rustiness.
He allowed the Portuguese only one more game in a lop-sided affair.
The 2022 US Open champion converted five of seven break points to continue his quest for a third title of the season after Indian Wells and Buenos Aires.
"Moving well, hitting the ball really well so I feel a lot of confidence playing here in Barcelona," said Alcaraz. "It's a really special place for me."
Norway's third seed Casper Ruud came through 6-2, 7-6 (7/1) against American Ben Shelton to set up a meeting with either Francesco Passaro or Francisco Cerundolo.
