Andy and Jamie Murray marked their first Davis Cup doubles match as a pair with a 7-5 6-2 6-0 victory over Laurent Bram and Mike Vermeer of Luxembourg.
Before a partisan Glasgow crowd, which included their grandparents, the Murrays won a tight first set 7-5 .
They then eased home for a win that gives Great Britain a 2-1 lead in the Europe/Africa Group II tie.
Britain will wrap up victory if Andy Murray beats Gilles Muller in the first of Sunday's two singles matches.
That would set up a third-round tie against either Belarus or Hungary in September and give Great Britain the chance of gaining promotion back to the World Group in 2013.
The Murrays were made to work for their win by the unfancied Luxembourg pair, who proved tough opponents in an edgy opening.
Bram and Vermeer saved four break points and a set point in the first set as Andy Murray squandered a good chance to wrap it up at 5-4 when his forehand split the Luxembourg pair but sailed just long.
However, in the 12th game Britain broke to love to clinch the set 7-5.
That proved pivotal and the Murrays then relaxed, breaking their opponents in the fourth game of the second set to take a 3-1 lead.
The Murrays broke for a second time to take the set 6-2, as the visitors' early resolve weakened.
Bram, who failed to win a single game in his singles defeat by Andy Murray on Friday, was broken twice in the final and the Murrays ran out easy winners.
The siblings were pleased to have got their Davis Cup partnership off to a winning start.
"It was brilliant," Jamie Murray said. "It was everything I expected and more. It took about four or five games for the goose bumps to go away.
"But it was an amazing experience. And to be able to do it with your brother is something we only dreamed of growing up."
World number four Andy Murray was equally satisfied.
"I thought it was good, we played a lot better in the second and third set," the Wimbledon semi-finalist said.
Meanwhile, there was an upset in Halmstad as Simon Aspelin and Robert Lindstedt of Sweden stunned Serbia's Wimbledon champion Novak Djokovic and teammate Nenad Zimonjic 6-4 7-6 (5) 7-5 in the doubles.
Djokovic entered the match at the last minute after withdrawing from the singles on Friday due to a knee injury.
France completed a 3-0, best of five, victory over Germany in the World Group after Michael Llodra and Jo-Wilfried Tsonga beat Christopher Kas and Philipp Petzschner 7-6 (7-4) 6-4 6-4 in the doubles.
And Spain beat the United States 3-1 in their World Group tie despite losing in the doubles after Bob and Mike Bryan defeated Fernando Verdasco and Marcel Granollers 6-7 (3-7) 6-4 6-4 6-4.
World number six David Ferrer wrapped up Spain's victory with a 7-5 7-6 (7-3) 5-7 7-6 (7-5) win over Mardy Fish, meaning that Andy Roddick and Feliciano Lopez did not need to contest the final rubber.