In other matches, Noah Rubin got past Mikhail Youzhny 6-4, 6-4, Tim Smyczek beat Ricardas Berankis 7-6 (4), 6-2, and Malek Jaziri defeated Evgeny Donskoy 6-4, 6-1.
Murray, 31, converted his seventh match point after more than two-and-a-half hours on court against the American. I was struggling on my serve and didn't feel like I had much rhythm.
The three-time grand slam victor, who withdrew from Wimbledon having lost to Nick Kyrgios at Queen's Club last month but beat Stan Wawrinka in Eastbourne before falling to fellow Brit Kyle Edmund, earned just his second victory of the year. He was the top seed in 2015 but lost his first match to Russian Teymuraz Gabashvili.
"I haven't played in the darkness or under the lights in a very long time and I felt like my rhythm was off on serve, my timing a little bit". I just want to have a prolonged period on the match-court right now.
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"I wasn't dictating numerous points".
Murray had surgery on his right hip in January, only returning to action on June 18, facing Nick Kyrgios at Queen's.
At 30-30 in the 11th game, McDonald stuck his racquet over the net to play the ball, losing the point on a violation quickly called by French umpire Arnaud Gabas.
Murray's first hardcourt match in almost 17 months 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.
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Both held serve until the ninth game, when McDonald sent a forehand wide to hand Murray the break and a 5-4 lead.
Murray made a slugging start in DC, where he was serving at just 48 per cent and was broken three times as McDonald took control and the opening set.
Murray said he wanted to enjoy being back on the tour, but the serious part - winning matches - was still extremely important to him.
He later overcame Stan Wawrinka at Eastbourne, only to lose in straight sets to Edmund two days later. Rubin now faces No. 2 seed John Isner, Jaziri plays No. 1 seed and defending champion Alexander Zverev, while Smyczek meets Zverev's older brother, No. 15 seed Mischa.
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Murray has been warming up for his return in the company of former England football captain Rooney, who joined him on court for a lighthearted session.