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It was a tight affair in the early stages of the first set as games went by the way of serve, with both struggling to clinch a vital break.
The first set was eventually decided by the way of tie-break, which Fognini was able to edge 8-6, despite some strong shots across the court from Bautista-Agut.
In the second set, both competitors grabbed a break point apiece in the early stages, but it was Fognini who moved on top with another break.
From then on, Bautista-Agut tried to get back on top, but 10th seed Fognini was able to break his serve and move into the next phase of the tournament.