Murray, the 2012 US champion and 2013 Wimbledon winner, looked fresh and strong in cool, breezy conditions as he rolled to a 6-3 6-3 6-4 victory at Arthur Ashe Stadium in his first meeting against the German.
The Scot, never broken in the one hour 46-minute match, ripped 36 winners, more than doubling the 17 unforced errors he was charged with.
"The second and third sets was good tennis, we had some fun points. I moved well tonight. I struggled a lot in my first match but I pulled up okay," said Murray.
"It was extremely windy today," he added. "That was the hardest part about the conditions; just very, very breezy and difficult to play close to the lines.
"But I hit the ball well considering, served better, and obviously I moved a bit better today, as well."
Faced by Bachinger, a contemporary of Murray's from junior days but now ranked 235 in the world, the British number one never looked like coming unstuck.
The German gifted Murray a break in the eighth game of the first set and from that point on the Briton was determined not to relinquish his advantage.
Having taken the opening set, Murray broke again early in the second and he went on to take a 2-0 lead with just an hour on the clock.
A glimmer of hope appeared for Bachinger soon after the start of the third set, but he failed to capitalise on the three break points he was presented with, as Murray roared back from 0-40 down to hold.
Murray had his chances to break at 4-3 ahead, but Bachinger held on. He was only delaying the inevitable, however, and Murray sealed victory with a break to love soon after.
Of his next opponent Kuznetsov, Murray said: “He’s had a couple of big wins in the Slams this year. He beat [David] Ferrer at Wimbledon and [Fernando] Verdasco here. I’ve never played him and don’t know his game that well, but I’ve seen him play a little bit.
"He hits the ball pretty flat, likes to go for his shots a lot. These courts are fairly quick, so that will probably suit him.”
US Open results
1-Novak Djokovic (Serbia) beat Paul-Henri Mathieu (France) 6-1 6-3 6-0
Pablo Carreno (Spain) beat Benoit Paire (France) 6-1 6-4 3-6 6-3
9-Jo-Wilfried Tsonga (France) beat Aleksandr Nedovyesov (Kazakhstan) 6-3 6-4 6-4
13-John Isner (U.S.) beat Jan-Lennard Struff (Germany) 7-6(5) 6-4 6-2
Sam Querrey (U.S.) beat 28-Guillermo Garcia-Lopez (Spain) 6-3 6-4 6-4
10-Kei Nishikori (Japan) beat Pablo Andujar (Spain) 6-4 6-1 (Andujar retired)
22-Philipp Kohlschreiber (Germany) beat Michael Llodra (France) 6-2 0-0 (Llodra retired)
5-Milos Raonic (Canada) beat Peter Gojowczyk (Germany) 7-6(4) 5-7 6-4 7-6(3)
Andrey Kuznetsov (Russia) beat 31-Fernando Verdasco (Spain) 6-3 4-6 4-6 7-5 6-3
Nick Kyrgios (Australia) beat Andreas Seppi (Italy) 6-4 7-6(2) 6-4
Victor Estrella (Dominican Republic) beat Borna Coric (Croatia) 7-6(2) 4-6 6-4 6-2
16-Tommy Robredo (Spain) beat Simone Bolelli (Italy) 5-7 6-7(5) 6-4 6-3 6-2
- Sports & Recreation
- Andrey Kuznetsov
- Fernando Verdasco