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The Scot, 28, beat world number 87 Taro Daniel 6-1 6-3 6-1 in his first match since becoming a father last month.
World number six Kei Nishikori brought the visitors level with a 6-3 7-5 7-6 (7-3) win over Dan Evans in Birmingham.
Victory in the best-of-five first-round tie will secure a quarter-final place and World Group status in 2017.
Dom Inglot and Jamie Murray are scheduled to take on Yoshihito Nishioka and Yasutaka Uchiyama in Saturday's doubles contest, although the line-ups can change up to an hour before the 14:00 GMT start time.
"We will wait and see," GB captain Leon Smith told BBC Sport. "[It will be] hopefully our strongest team, put it that way."
Britain are defending the title they regained last November for the first time in 79 years with victory against Belgium.
"It was amazing," Murray said of the reception he received after needing only 90 minutes to see off Daniel.
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There were signs of rustiness - four double faults and 25 unforced errors slowing his progress at times - but the Scot broke serve six times and saved both break points he faced in a one-sided win.
Murray, 28, won the opening 11 points in his first match since losing to Novak Djokovic in the Australian Open final 33 days ago.
He wrapped up the first set in 28 minutes and took hold of a more competitive second after a double fault at 3-3 from Daniel, the US-born 23-year-old with just five ATP wins to his name.
Two blistering returns gave Murray the decisive break at the start of the third and he wrapped up the 28th Davis Cup singles win of his career in style.
"The last few weeks have been the best of my life, really special," Murray said of becoming a father to Sophia.
"It has been tough the last few days being away from her for the first time but it had to happen to some stage, and it is a pleasure to represent my country and be with team-mates that we won with last year.
"The second set was tough - a lot of close games and some tough points, which was good for me.
"I was getting a little out of breath but I played a good match, served well, missed a few second serves but the first serve went extremely well, so it was a nice start."
Evans, from Solihull, had the support of his home crowd and the confidence from a victory in his only previous meeting with Nishikori, but the Japanese player was still too strong.
It is over three years since he surprisingly lost to Evans at the US Open and Nishikori has since become established among the game's elite.
Evans, 25, once again played above his ranking of 157 but could only convert four of 13 break points that came his way.
After dropping serve twice in the first set he failed to capitalise on 0-40 early on in what proved to be a tight second.
Both players missed break point chances and a tie-break loomed with the Briton serving at 6-5, but after saving two set points he then netted a volley and double faulted.
With both men apparently tiring, the third set saw a rash of service breaks - six in eight games - with Evans unable to build on leads at 3-2 and 4-3.
Nishikori, 26, was similarly vulnerable on his own serve but got himself across the line in the tie-break after two hours and 44 minutes.
Andy Murray slipped fairly seamlessly back into the day job, but Kei Nishikori had to absorb a lot of pressure from Dan Evans to make sure the tie is level heading into Saturday's doubles.
But who will play? Murray told me he "would love to play if it's the best thing for the team," as long as his body feels fine in the morning. But will Nishikori be on the other side of the court? It is looking likely - even though he has only ever played two Davis Cup doubles matches for Japan.
"He missed a few balls and looked a bit rusty but overall you've got to give Andy a 9/10. He just wanted to feel the ball out there but he looked sharp, and will be looking forward to the big match against Nishikori on Sunday.
"Nishikori got very nervous against Evans for a while there, but in the end the class player came through and upped his game."
Friday
Andy Murray beats Taro Daniel 6-1 6-3 6-1
Kei Nishikori beats Dan Evans 6-3 7-5 7-6 (7-3)
Saturday doubles
Dominic Inglot & Jamie Murray v Yoshihito Nishioka & Yasutaka Uchiyama
Sunday
Andy Murray v Kei Nishikori
Dan Evans v Taro Daniel
Listen to State of the British Game - a 5 live sport special
Andy Murray returned to action with a comfortable win as Great Britain ended day one of their Davis Cup defence tied at 1-1 against Japan in Birmingham.