The pair combined on Friday to claim a 2-1 place in the title match at the 22nd edition of the eight-nation, mixed-team competition with a defeat of Russians Elena Dementieva and Igor Andreev in a 6-4, 6-7(6), 10-6 match tiebreak.
In the singles matches, world number four Murray swamped Andreev 6-1, 6-0 in less than an hour while Dementieva schooled 15-year-old Robson 6-4, 6-0 to leave the tie on one rubber apiece.
After winning the doubles, however, Robson, the junior Wimbledon winner, seemed particularly excited by the pair of diamond-encrusted tennis balls awarded to the winning team in addition to prize money.
And the young millionairess-in-the-making is quickly acquiring champagne tastes: "I got my revenge in the doubles," Robson said. "I want those diamonds."
Informed in an on-court interview that her mother might have laid claim to them, the teenager added: "No, way, there's no chance mum's going to get the diamonds."
Iberians Maria-Jose Martinez Sanchez and experienced Tommy Robredo would provide more than enough competition for the Britons.
Murray beat Robredo twice in 2009 but lost to him indoors in a 2007 final.
"He's played great here this week," Murray said. "Laura has her chances in singles, and I want to win those diamonds now also."
Robson said that after winning a practise match at the Burswood Dome against Martinez Sanchez before the start of the Hopman Cup, she would take that as a "victory." "For me, it's 1-0 now," she joked.
The British victory eliminated the possibility that qualifier Kazakhstan could slip in to claim the finals spot for the group. The outsiders did make an impression, however, with a 2-0 sweep of Germany.
Yaroslava Shvedova beat Germany's Sabine Lisicki 6-4, 7-6 (7-3) while Audrey Golubev defeated Philipp Kohlschreiber 6-2, 6-2.
In the British-Russian mixed tie, Robson and Dementieva played the more active roll in the deciding match tiebreak, which comprised the final set, after Murray and his partner were unable to go through in straights while leading a set and 3-1.
Murray and Robson took a 4-0 lead in the final tiebreaker with the Russians closing to 4-7.
A Murray overhead a few points later yielded three match points with a Scottish winner ending the contest. Britain provided a dozen aces and 27 winners, breaking four of nine times.