Game 5 proved pivotal in the first set as Pliskova broke the Watson serve to move into a 3-2 lead which she then saw out to take it 6-4.
Highlights of Watson's fightback to beat Pliskova
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But Watson stormed back in the second as she went a break up in a tense eighth game before finishing off the set with an ace.
And the world number 75 carried that momentum into the third by double breaking her Russian opponent en route to sealing her place in the second round.