Having started the final day locked at 45-45, the Bulldogs pulled 58-49 ahead, needing just two more points for victory.
But wins for Dan Evans in singles and Andy Murray and Naomi Broady in doubles set up a winner-takes-all doubles finale.
Joe Salisbury and Harriet Dart won the contest 6-3, 6-2 against Jamie Murray and Heather Watson to seal a 63-56 victory for Bulldogs.
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British No 1 Johanna Konta did not play for the Bulldogs on the final day and wasn't seen in attendance, although her team-mates did find a cardboard cut-out of her to join the celebrations.
With the score level after six days of action, Maia Lumsden put the Bulldogs ahead in the first match of the day as she beat Alicia Barnett 6-3, 6-3.
Anton Matusevich replied for the Union Jacks with a 6-3, 6-2 win over Alastair Gray, but the momentum swung back in the Bulldogs’ favour as Emma Raducanu won 6-3, 6-3 against Naomi Broady and Liam Broady won a tight tussle against Ryan Peniston 7-6 (7-1), 3-6, 12-10.
Broady, 26, said he has loved the team experience - despite some heckling from the sidelines.
"It's an ultra-competitive environment but I think it's brought out the best in us and I can tell you now, I'm not going to be that nervous again for a long time.
"The pressure from the side of the court when you've got Sir Andy Murray and Dan Evans chirpsing you about how many forehands you've missed in the match…I'm just glad I got through it!”
Kyle Edmund extended Bulldogs’ lead to 55-47 with a 6-2, 6-1 win over Jan Choinski, but Union Jacks’ Watson continued her fine form as she beat Beth Grey 6-0 6-2 to stay unbeaten in singles.
Harriet Dart moved the Bulldogs two points from victory with a 6-4, 7-6 win over Jodie Burrage, only for Union Jacks to battle back again.
Evans won 7-5 6-2 against Aidan McHugh before Andy Murray and Naomi Broady beat Edmund and Raducanu 6-3, 7-6 (7-5) in the penultimate doubles match.
That meant it all came down to the final doubles match and Salisbury and Dart proved too strong for Jamie Murray and Watson.
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