The 35-year-old Swiss won 6-3 6-4 in 55 minutes to reach the last 16, where he will face Spanish 14th seed Roberto Agut.
Federer has never lost a set to Bautista Agut in their previous five meetings, but Federer insists he is not taking anything for granted.
Bautista Agut had rallied to beat American Sam Querrey 3-6, 6-2, 6-3 on Monday.
“Querrey was playing so well the first set, I thought at some point he was going to steamroll, but Bautista Agut competes so well point for point, day in and day out,” Federer said.
“He plays a ton of tournaments, and he’s just really match tough,” Federer added
Czech 10th seed Tomas Berdych beat Luxembourg’s Gilles Muller 6-3 6-4 and goes on to play Frenchman Adrian Mannarino.
In other matches Swiss top seed Stan Wawrinka beat Tunisian Malek Jaziri in two straight sets, 6-3 6-4, while David Goffin also overcame Diego Schwartzman in three sets, 4-6 6-3 7-5.
Wawrinka will next play 19-year-old German Alexander Zverev on Tuesday.
Zverev beat American John Isner in a 6-7 (7-5), 7-6 (9-7), 7-6 (7-5) thriller. Isner served 28 aces, but it wasn’t enough, Miami Herald reported.
One of the thrillers of the day saw Australian Nick Kyrgios tame hard serving Ivo Karlovic in tight three sets, 6-4 6-7 7-6.
In the late-night match, 36-year-old Venus Williams — the oldest woman in the draw — beat Svetlana Kuznetsova 6-3, 7-6 (7-4). The final two points of the match featured long rallies and brilliant shotmaking.
Williams is a three-time champion here and first played Key Biscayne as a 16-year-old in 1997. Her opponents included Martina Hingis and Jennifer Capriati.
“I was still in braces, it’s been a long time,” Williams said, smiling, in her post-match interview.
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