The Scottish brothers missed three match points before sealing a 6-4 6-7 (7-9) 10-5 win at the Washington Open.
They trailed 5-2 in the decider – a first-to-10 champions tie-break – but won eight straight points for victory.
Andy Murray, 32, is playing his fourth event since hip surgery in January.
The former world number one feared his career might be over before having the hip resurfacing operation, but returned to the doubles court five months later when he won the Queen’s title alongside Spain’s Feliciano Lopez.
The three-time Grand Slam champion says he could make a singles return at the Cincinnati Masters later this month and looked in the best shape he has been since resuming his career as he won alongside his older brother Jamie.
Andy Murray’s demeanour on his return to the American capital was markedly different to 12 months ago when, struggling to cope with the pain in his hip, he broke down in tears at the end of his third-round singles winagainst Marius Copil at about 3am local time.
Now he is pain free – looking happy on court and as fiercely competitive as ever – as he continues towards his goal of returning to singles action.
“I’m in a much better place than last year – physically I feel better, I’m not restricted in hitting shots, I’m still a bit slow but hopefully that will improve,” he said.
“To come back here and be pain free is brilliant.”
The Murray brothers, who won doubles titles together in Valencia in 2010 and Tokyo in 2011, complemented each other well as they impressed with their quick reactions around the net and solid serving.