Robson and Murray paired up for the first time to come through the mixed doubles
Britain completed a 2-1 victory against Kazakhstan in the Hopman Cup after a gruelling triumph in the mixed doubles.
After Laura Robson's opening defeat, Andy Murray swept aside the world number 133 Andrey Golubev to win 6-2 6-2 in the eight-team competition.
Murray and Robson then beat Golubev and Yaroslava Shvedova after a 12-10 final set win in the champions tie-break.
Britain, seeded third at the round-robin event, will face Germany on Wednesday and Russia on Friday.
Australia, Spain, Romania and the USA contest Group A.
The winners of the two groups will go through to the final on 9 January.
I'm kind of proud of my volleys in the tie-break, they're the only ones I made!
Britain have not played in the event since 1992, when Jo Durie and Jeremy Bates led the challenge, and Robson and Murray seemed to relish a rare chance to play mixed doubles.
Asked what had happened in the second set, Murray quipped: "I'm going to blame her a little bit though because she started asking me if I moisturise my hands and I think maybe she lost her concentration just a little bit
"But she's only 15 so I'll let her off. It was fun. She hit me on the back at one point - I don't think I really deserved that... it was sore already because I was carrying her!"
Robson matched her senior partner in the banter department with a nice line in self-deprecation and responded with: "I'm kind of proud of my volleys in the tie-break, they're the only ones I made!
"I will take out of the evening that I should work more on my serve and we should communicate more so that he doesn't hit me!"
Murray has this year changed his preparation for the Australian Open, which begins on 18 January, as he targets an elusive maiden Grand Slam title.
The Scot has in the past played at the Qatar Open in Doha, but instead headed straight for Australia after completing his traditional three-week training camp in Miami.
And, playing his first match of the new year, the 22-year-old world number four got off to a flier against Golubev, securing an early break in the fourth game.
Murray conceded only one point on his service in the opening set before breaking again to clinch it in 28 minutes.
"It was perfect, he made me do a lot of running and there were lots of fun points in there," said the world number four.
"This is great preparation for the Australian Open because you get at three singles matches and three doubles and you hit a lot of balls, whereas you could just lose in your first match in the other competitions going on this week."
Robson's debut in the competition did not run quite so smoothly, although she did take the first set from the flu-ridden world number 52 Shvedova.
The Briton was cruising when her Kazakh opponent called a five-minute medical time-out at the end of the set, but Shvedova fought off illness to win the final eight games and secure victory.