Murray, fresh from his US Open mixed doubles win with Bethanie Mattek-Sands, and partner Dom Inglot overcame Denis Istomin and Sanjar Fayziev 4-6 7-6 (10/8) 6-2 6-3.
Their victory, in two hours and 54 minutes, means Great Britain take a 2-1 lead into Sunday’s reverse singles.
With the Davis Cup undergoing a revamp next year there is no relegation at stake but Leon Smith’s team need a victory in the tie to ensure they are seeded in February’s qualifying tournament.
The Glasgow crowd gave their man a rousing reception but the party was in danger of falling flat when a solitary drop of serve from Murray allowed the Uzbek duo to claim the opening set.
With the doubles so often pivotal in the Davis Cup, the tension was palpable in the second set.
Inglot was holding his end up with regular serves of 130 miles per hour, but his returning was erratic at best.
The set went to a tie-break and amid a flurry of poor service returns and unforced errors Istomin netted and Murray and Inglot levelled the match.
Almost two hours had elapsed before the Britons secured their first break of the match on the Fayziev serve, courtesy of a delightful sliced backhand from Murray.
Fayziev seemed to be tightening up while Istomin, the only man on court who played on Friday, a five-set defeat to Dan Evans, was looking a little weary.
The double break was secured, again via Fayziev’s serve, and Murray held to take the third set.
At 2-2 in the fourth the Fayziev serve was once again under scrutiny and once again it buckled, an Inglot backhand down the line sealing the deal to love.
The momentum was firmly with the home side and they broke Fayziev once more to wrap up the victory.
Murray said: “We were fighting hard in the first couple of sets but couldn’t quite find a break.
“We were so close to being two sets to love down, but then we relaxed a bit and played really well in the last two sets.”