The Swiss great had won five previous matches against Bautista Agut without dropping a set, and that continued with a 7-6 (7-5) 7-6 (7-4) victory.

Federer, a two-time champion in Miami, was well below the blistering form he has shown throughout this year, but he was still too good for the Spaniard.

The 18-time grand-slam winner mixed 30 winners with 32 unforced errors, setting up a last-eight clash against Tomas Berdych.

Federer, the fourth seed, appeared in complete control early, cruising through his service games and putting Bautista Agut under pressure.

But that took an unlikely turn in the ninth game, the Spaniard breaking for a 5-4 lead.

Bautista Agut failed to consolidate, however, broken to love when he sent a second serve wide.

Federer was tested in the tie-break but came through to take the opener, his 13th straight set won against Bautista Agut.

He broke to start the second set when 14th seed Bautista Agut sent an overhead long to end an eight-minute first game, only for Federer to hand back that advantage.

The set proved to be a grind for Federer, who eventually closed out his win in yet another tie-break.