Third-seeded Murray, who ended his country's 76-year wait for a Grand Slam men's champion when he won his maiden major title in New York last year, eased past Germany's world number 49 Florian Mayer, 7-6 (7/2), 6-2, 6-2. His win was built on an impressive 42 winners and seven aces.
"I think I need to start my matches quicker than I have been doing. I am not that fast out of the blocks," said the 26-year-old. "But once I got going I was striking the ball cleanly."
Istomin will be playing in the last 16 in New York for the first time after ending Seppi's perfect streak of seven five-set wins in 2013. Two of those came against him at the Australian Open and Wimbledon.
Murray defeated Istomin in their only match in the quarter-finals at Brisbane in January this year.
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Meanwhile, Hewitt reached the fourth round of a Grand Slam for the 30th time with a 6-3, 7-6 (7/5), 6-1 win over Russia's Evgeny Donskoy.
"It's always great to come back to New York where it all started for me -- I won the doubles in 2000 and singles in 2001. I have played some of my best tennis here," said Hewitt, who claimed victory on a third match point.
"I think the crowd supports me because my personality is the joy of coming out to play. I feel pretty good. I have had three tough matches where I have had to keep bouncing back all the time.