The world No 4 dropped his opening service game and then trailed early in the first-set tie-break but he pulled through and from then on there was only one winner.
In round two Murray will face big-hitting Dutchman Robin Haase, who has won their only previous meeting and could prove to be a tricky opponent for the Scot.
Murray and Devvarman were meeting for the first time but the British No 1 had an insight into the Indian’s game from friend Dani Vallverdu, who is a key part of the 24-year-old’s coaching team and who faced Devvarman in college tennis in the US.
The 26-year-old is ranked 64th in the world and is yet to pull up any trees on the ATP World Tour but he made a very positive start and immediately put Murray under pressure on his serve, forcing his opponent to battle back from 0-40 and then taking a fourth break point.
The Scot is often a slow starter, though, and any concern that the first set might slip away from him were allayed when he broke back at the third time of asking in the sixth game.
It was an entertaining contest, with Devvarman eager to come to the net while Murray was timing the ball pretty well on his groundstrokes. The fourth seed would have been frustrated not to finish off the set before the tie-break after having openings in a number of Devvarman service games, but the Indian held on and some sloppy play from Murray saw him trail 3-1.
But again he addressed the issue quickly and two big serves helped him create three set points, of which he took the third when Devvarman netted a forehand he really should have made.
Murray made the perfect start to the second set with a break in the opening game only to give his advantage back in sloppy fashion with a double fault.
But the world No 4 was clearly in the ascendancy now, his groundstrokes just too powerful and accurate for Devvarman, and Murray broke again in the fifth game, this time to love with a trademark backhand down the line.
Devvarman’s chance looked to have gone and Murray made it four games in a row with a second successive break before serving out the set.
Murray looked in a hurry to get the match finished and, although he was still not playing at his best, it was far too good for Devvarman.
A break in the opening game of the third set cemented his advantage and he extended his run of games to eight with a second, dragging his opponent from side to side and then finishing off the point with a volley.
The Indian at last got on the board in the fifth game, and he was given a reprieve when Murray missed a match point serving for it at 5-2 and was promptly broken. It was only temporary, though, Murray sealing victory on his next opportunity.
It was a decent enough performance from the Scot as an opening effort but he will know he must cut down on a tally of 44 unforced errors.
Laura Robson felt too many unforced errors and a lack of experience were the crucial factors in her second-round defeat by 30th seed Anabel Medina Garrigues yesterday. The 17-year-old British No 4 was on a four-match winning streak after coming through qualifying at Flushing Meadows but she found gritty Spaniard Medina Garrigues just too consistent.
Robson had plenty of successes, particularly on her big forehand, but 32 unforced errors more than cancelled out the 20 winners as she went down 2-6 3-6.
After a run of four successive games gave Garrigues the opening set, Robson had her only two chances to break leading 3-2 in the second but she could not take them and the Spaniard capitalised in ruthless fashion.
Robson said: “I’m obviously really disappointed because it was quite clear I just made too many mistakes.
“I think I tried to go for too much. I felt like I had to get in there first. She played really tactically smart.”
The teenager was happy with her efforts in New York, though, and has no plans to rein in her attacking tendencies.
She said: “I’ll take a lot of positives. It was my first time qualifying for a grand slam and I won a round. I’m still happy with the way I’m playing, I think she just had more experience and that showed.
“I will always play aggressive tennis, I think that’s the game that suits me. Just because I miss a few here and there doesn’t mean I should go defensive all of a sudden.
“I had things I said I wanted to improve on after Wimbledon, one of them being consistency, and I think that’s still the main thing I can work on, and just continue to get fitter and faster and start working on my tactics.
“Before I just went out there and played but now I think I’ve got enough options with my shots that I can do various different things.”
Robson, who is still limited by the amount of senior tournaments she can play because of her age, is likely to rise to around 150 in the world rankings thanks to her run in New York.
Venus Williams yesterday withdrew ahead of her second-round match against 22nd seed Sabine Lisicki. The American has not played since Wimbledon because of a virus.