The Spaniard took a while to get going, surrendering the opening set in 35 minutes but he turned the tables in sets two and three, prevailing in an hour and 39 minutes on a sun-scorched Auckland Centre Court. He will face Sam Querrey or Jiri Vesely in the last eight.
Bautista-Agut has endured a shaky start to 2018, plummeting out in the second round in Pune last week, and the opening frame raced away from the 29-year-old as he searched for answers.
He found himself in a 0-30 hole in the third game of the set as he netted consecutive forehands and he was rocked by Johnson’s eagerness to approach the net.
The American broke for a 3-1 advantage and Bautista-Agut soon found himself a double break down as Johnson punished his hesitancy. The latter was mixing his backhand’s returns to good effect, frequently dropping balls short while stepping inside the baseline and arrowing winners down the line.
Johnson wrapped up the set without relinquishing a single break point but the Spaniard roared back in set two, breaking the 28-year-old in his very first service game.
He consolidated the break of serve for a 3-0 buffer and he raced out to a 4-1 advantage having dropped only two points since the start of the second set.
Johnson briefly threatened to restore parity when he forced the only deuce of the set but Bautista-Agut remained composed. More willing to draw Johnson to the net instead of attempting to punctuate through his backhand slice, he leveled the match as the clock ticked past the hour mark.
It was all to play for in the deciding set but Johnson, still smarting from the momentum shift in the previous set, fell back into old habits.
The break of serve was coughed up at the same juncture as set two and it was a hefty backhand from the Spaniard which drew the error at the net.
Thereafter Bautista-Agut seemed to hold the American at arm's length and his place in the quarterfinals was all but sealed when he broke the Johnson resolve for the fourth time in the match, unloading on a forehand winner that kissed the far sideline.
Match point arose and Johnson, scrambling to recover his court position, bunted a forehand into the net.