Konta made a sluggish start, going 3-0 down, and the Swede deserved her 6-3 lead in the first set.
But the former world number four made a strong comeback, opting for short balls, getting her opponent to move more, and levelled things up when she took the second set 6-3.
It looked like it might be Peterson who would be rueing missed opportunities in the decider, going 4-1 up before allowing Konta back into it at 5-5.
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But she kept her cool and concentration, serving well to take the match 6-3, 3-6, 7-5.
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