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One of Murray's four first-set double faults surrendered a break in the third game and Murray's seventh consecutive lost second-serve point gave McDonald a 3-2 edge when the American hit a forehand victor.
"It was a tough, tough match", Murray said.
Murray's first hardcourt match in almost 17 months, delayed three hours by rain, turned when he broke in the penultimate game of the second set and again on his fifth break chance in the opening game of the third set.
In the next game at 30/30, when it appeared the American had an easy putaway volley to earn a game point, he was called for reaching over the net, giving the Scot break point.
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Murray quickly found himself serving for the match at 5-4 with McDonald rolling the dice, realising that if he was going to lose, he would go down fighting.
He took part in the Queen's Club and Eastbourne events earlier in the grass-court season, losing to Edmund at the latter, but a reunion is on the cards on the hard courts of the U.S. capital providing Murray overcomes a player who reached the fourth round of Wimbledon.
[ALSO LIKE] Murray held five match points while serving for the match for the first time at 5-4 in the third set, but McDonald was steady, breaking back.
"I hadn't played in darkness or under the lights in a really long time and I felt my rhythm was off", Murray said. He will face compatriot Kyle Edmund next. "I've never met him before, so it's very cool".
Elsewhere American Tim Smyczek won his rain-interrupted match against Lithuanian Ricardas Berankis 7-6 (4) 6-2 and will next face Mischa Zverev, who defeated Smyczek in three sets at the Atlanta Open last week. There was still another match left to go in the main stadium, and it involved another three-time major champ: Stan Wawrinka, who faced American qualifier Donald Young.
He walked awkwardly around the court between points, especially in the lengthy third set when at one point he grabbed his hamstring and winced in pain. His lone win on grasscourts came over Swiss Stan Wawrinka, another three-time Grand Slam victor fighting back from injury.
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