The Olympic gold medallist had been scheduled to face Gael Monfils in the first round of the £800,000 hardcourt event but the Frenchman pulled out with a knee injury.
Murray was given a workout by 6'10" Karlovic and was forced into a tie-break in the first set which the Scot took 9-7 with a superb running forehand pass down the line.
A quick change of wardrobe and Murray, now all in black, waited for his moment in the second, converting his third match point with a vicious backhand to the Croatian's body after an hour and 38 minutes.
Karlovic, who faced Marco Chiudinelli - a 7-6(3) 6-2 victor over Martin Klizan on Tuesday - in the final round of qualifying at the weekend, sent down 18 aces in all. However Olympic champion Murray, playing in his first tournament since breaking his country’s 76-year men’s Grand Slam drought at Flushing Meadows, did not face a break point against the world number 79.
"I was so, I don't want to say 'obsessed' with winning a grand slam, but it was so important to me," world number three Murray said.
"Sometimes during the year in certain matches I haven't done myself justice. I felt after the US Open (I needed to) reset some goals.
"I was always focusing on the next grand slam rather than every tournament and every match I played.
"Now I feel like I can hopefully concentrate better, take more responsibility for my performances in every tournament throughout the year."
The Scot said he felt no different having finally won his first grand slam after losing in four finals.
"It didn't feel a whole lot different (stepping on court as a grand slam winner)," said the 25-year-old.
"Hopefully with time that will come," added Murray, who reached his first Wimbledon final this year before exacting his revenge on Roger Federer in the Olympic final in London.
"I think where I will feel it more will be if I'm getting to the latter stages of grand slams. Hopefully I will start feeling more confidence to go on to win."
Murray, who was on court for an hour and 38 minutes, will face Slovakia's Lukas Lacko in the second round.
Fifth seed Nicolas Almagro lost two tie-breaks to bow out 7-6(4) 7-6(5) to wildcard Tatsuma Ito. Ito edged a close match which saw only one break for each player despite seven chances for Almagro and five for Ito.
Qualifier Dmitry Tursunov lies in wait for Ito after he beat Bernard Tomic 6-4 7-5.
Japan's Kei Nishikori survived a fright against countryman Go Soeda, the eighth seed squeaking through 4-6 6-2 6-3 to the relief of Tokyo organisers in two hours and 29 minutes.
Nishikori, who reached his first semi-final of the year in Kuala Lumpur last week, next plays Spaniard Tommy Robredo, a 6-2 6-4 winner over Finland's Jarkko Nieminen.
Big-serving Canadian Milos Raonic hit 10 aces in a 6-4 6-4 victory over Czech Radek Stepanek, the world number 15 and sixth seed moving through to face Serbia's Viktor Troicki.
Second seed Tomas Berdych will play Alejandro Falla in the second round after the Colombian beat Thomaz Bellucci 7-5 6-2. Jeremy Chardy of France beat wildcard Yuichi Sugita 6-1 7-5 while Marcos Baghdatis overcame Sergiy Stakhovsky 7-6(3) 7-5.