The Olympic champion was a different class to the overmatched Dodig, with Murray wrapping up a 6-2 6-1 6-3 second-round victory in just an hour and 51 minutes.
The performance was a marked improvement on Murray's first-round performance - where the Scot had looked shaky despite dropping just seven games against Alex Bogomolov en route to victory.
Dodig battled gamely on Arthur Ashe Stadium, but the world No.118 failed to show little of the form that saw him challenge the top-30 at one point last year and topple Rafael Nadal.
Murray broke the Croatian twice to take the opening set, before taking three of his four break-point opportunities in the second.
The Scot said: "It was better than the first round, that's for sure. It was pretty comfortable conditions out there today. There wasn't really any wind, it was fairly cool as well. That helped.
"I moved better than I did in the first match and served better, and I was able to dictate more of the points because of that. I was much happier with the way I played."
The 25-year-old was pleased his homework had paid off, saying: "I watched a few clips of him playing the last couple of days. I knew he liked to come forward a lot.
"When he's up there, he likes to hit drop volleys as well.
"When I saw him coming into the net, I tried to move forward in the court and managed to chase down a few of the drop volleys. When you're expecting something, it makes it much easier to play against.
"When he first came on the tour, not many guys will have seen him. When someone serve-volleys and comes into the net a lot, it's tough nowadays, you don't see it that often."
The 25-year-old third seed broke again in the fourth game of the final set - but the biggest threat to his hopes was his own focus.
"I always wanted to play the night matches at the US Open," he said. "I've always enjoyed them. I've had some good wins against tough players.
"The conditions are nice. It's a good atmosphere to play in. There's a good energy on the court, that's why I've played well."
Murray will now face either 30th seed Feliciano Lopez or Pablo Andujar for a place in the last 16.
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Fourth seed David Ferrer passed a potentially dangerous test with flying colours as he beat big-serving South African Kevin Anderson in the first round of the US Open.
Ferrer has been elevated into the top four because of the absence through injury of his fellow Spaniard Rafael Nadal and is seeded to meet Novak Djokovic in the semi-finals.
Although he is more renowned for this exploits on clay, Ferrer has had just as good results on hard courts and reached the last four in New York in 2007, losing to Djokovic.
At 6ft 8in tall, Anderson is not an opponent to be underestimated, but Ferrer was in control throughout and won 6-4 6-2 7-6 (7/3) to set up a second-round meeting with Dutchman Igor Sijsling, who beat Daniel Gimeno-Traver 7-5 6-3 6-4 on Wednesday.
Ferrer was very content with his performance, saying: "I feel good. It was not an easy match. He's a really good player, he has a very strong first and second serve. I'm happy because I played good in my first round."
Serbian 29th seed Viktor Troicki went out in the first round, losing 6-4 6-4 3-6 6-2 to Germany's Cedrik-Marcel Stebe.
Eighth seed Janko Tipsarevic looked like he was on his way out when he trailed French wild card Guillaume Rufin by two sets but the Serb fought his way back to win 4-6 3-6 6-2 6-3 6-2.
Luxembourg's Gilles Muller then became the eighth player this tournament to recover from such a situation to beat 28th seed Mikhail Youzhny 2-6 3-6 7-5 7-6 (8/6) 7-6 (8/6).
The success of America's Brian Baker has been one of the stories of the season and he was a 6-3 6-4 6-2 winner over Jan Hajek on Wednesday seven years after his last US Open victory.
The 27-year-old was one of the world's top juniors and was beginning to make progress when injuries struck, ruling him out of the game for six years.
Most people thought Baker had retired but he gave the game one last go last autumn and was so successful that he is now ranked 70th and reached the fourth round of Wimbledon as a qualifier.
Del Potro, who has been struggling with a left wrist problem, had been due to face fellow Argentinian David Nalbandian but he withdrew citing a rib injury.
The matches on Arthur Ashe Stadium were very one-sided over the first two days but the crowd certainly got their money's worth from the contest between home favourite John Isner and Belgium's Xavier Malisse.
Isner eventually came through 6-3 7-6 (7/5) 5-7 7-6 (11/9) while Malisse treated umpire Carlos Ramos to an ongoing tirade relating to a number of line calls, including a foul-mouthed rant at the end of the second set that earned him a formal warning.
Ninth seed Isner, who came into the tournament as one of the form players after winning the title in Winston Salem last week, said: "I knew the match today [Wednesday] was going to be tough.
"A lot of people are projecting me to go far here, but I wasn't looking past this match. As you guys could see, I had my hands full. He doesn't mind playing me. He's played me well in the past and he did it again today.
"It got to a certain point there where it was anyone's match. I just got pretty fortunate at the end."
France's Richard Gasquet, the 13th seed, had to come from a set down to beat Albert Montanes 4-6 6-2 6-3 6-3, while Spain's Tommy Robredo, playing his first grand slam tournament of the year after injury, knocked out 26th seed Andreas Seppi 6-1 7-5 6-3.