Murray and Soares trailed their distinguished opponents by a set and 4-1 at the O2 Arena, although only after a dramatic collapse that saw them spurn three set points and a 5-3 lead.
They fought back to take the second set but a topsy-turvy contest turned again in the deciding tie-break as the Bryans recovered to win 7-5 6-7 (3/7) 10-8.
Murray, sporting a Union Jack wristband, is the only British representative here while his younger brother Andy remains out injured and, but for an sudden lapse in concentration, this was a match he and Soares should have won.
They were faster and sharper than their opponents early on and after clinching a break at 2-2, they looked firmly on course to win the opening set.
But they imploded at 5-4 and a glaring miss from Soares was the catalyst as he slapped a gift of a volley long to spurn the first of three set points.
The Bryan brothers defended the next two as well, with the last securing the break back given deuce in doubles here acts a sudden death point.
Still reeling, Murray and Soares struggled to recover as Mike Bryan held to love for 6-5 before two Soares double faults and a missed Murray volley conceded the set.
The Bryans then steamed into a 4-1 lead in the second but the tide was finally stemmed at 4-2 as a superb Murray lob helped seal the break back.
Into the tie-break, where two crisp volleys sent Murray and Soares 4-1 ahead and they took the second of four set points when Mike Bryan returned long.
The match would be decided in a first-to-10 tie-break but this time it was the Bryans who started fast, storming into a 4-0 lead.
Murray hurled his racket into the ground after some overly-generous volleying allowed his opponents to move 6-2 ahead and then 9-5, to open up four match points.
Mike Bryan missed one chance on his serve and Murray saved two more on his own, but Bob Bryan thwarted the comeback as his brother's volley finally sealed victory.