The World No 4, appearing for the first time since he reached the US Open final, hammered Austria’s Alex Peya in straight sets to level the scores at 1-1 in this world group qualifier.
After clinching a 6-4 6-1 6-3 win, Murray pretended to strangle himself after a dig from Jurgen Melzer.
The Austrian No 1 suggested in the build-up that the British star could buckle under the pressure from an expectant home crowd having done so well at Flushing Meadows.
But after such a straight-forward win, Murray is likely to partner brother Jamie in today’s doubles against Melzer and Julian Knowle.
Then tomorrow, Murray will play World No 41 Melzer, who came within two points of winning their third-round US Open clash.
There is clearly no love lost between the pair. Murray said: “Yes, Melzer has fired me up a little bit.
“It is not nice when a fellow competitor makes suggestions about these sort of things.
“The top five, top 10 players, deal well with the pressure and they win big matches.
"That’s why, when I was two sets down and two points away from losing to Melzer, I played some of my best tennis to get myself back into the match.”
While Ross Hutchins was down to partner Jamie Murray, the British team will be keen for their top star to play as they look to go 2-1 up.
The plan will then be for Andy, 21, to clinch the tie to avoid a potentially nerve-shredding final rubber between Alex Bogdanovic and Austrian No 2 Peya.
Murray added: “I will do whatever is the best for the team. I’ve a good Davis Cup record in doubles but have not played with Jamie or Ross.
“The doubles is 50-50. Julian and Jurgen have played much more than any of our doubles combinations. But if we win, we will be strong favourites overall.”
Bogdanovic showed he has talent but is still mentally fragile — crashing 6-3 6-7 2-6 1-6 to Melzer despite a great start.
He has now lost all five of his live Davis Cup ties but the Brit insisted: “Physically, I was not tired but perhaps I was mentally.”
Davis Cup captain John Lloyd said: “I’m still very confident we will beat Austria.”