Wrongly convinced, as it turned out, in what felt like a possible turning point in a match that Burrage, a wildcard, had been dominating.
That it proved to be anything but is a testament to Burrage's tenacity and composure, as the world No 108, who had not made it past the first round here in two previous attempts, reeled off the next four games to complete a 6-1, 6-3 defeat of a player ranked 41 places in front of her.
It was not entirely wobble-free in the closing stages, as she was hauled back from 40-0 to deuce in the final game, but Burrage closed it out at the fifth attempt, reading and reaching a drop shot before flashing a cross-court winner.
"There was a lot of relief [at the end]," Burrage said. "Obviously it took me a few match points to get over the line. But I'm very happy with how I played and how I handled myself on court. I really enjoyed every moment of it.
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