The American twins looked out of it when they trailed 9-5 in the deciding championship tiebreak but used all their craft, and some luck, to claw back the deficit and qualify at the expense of the Anglo/Australian duo.
It was their 35th victory in the year-end championship -- taking them past the record they had shared with Daniel Nestor.
A nerve-jangling scrap ended when the Bryans converted their fifth match point -- but the match will haunt Peers who blazed a forehand long with the court gaping at 9-8.
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Murray, who will be alongside brother Andy in Britain's Davis Cup team for next week's final against Belgium in Ghent, is splitting with Peers after three years together having reached the Wimbledon and U.S. Open finals this year.
The 37-year-old Bryans, who have won a record 109 titles together, have now reached at least the semi-finals of the season-ender for the 10th time, winning four titles.
They go through as runners-up in their group and will find out their semi-final opponents on Friday.
(Reporting by Martyn Herman, editing by Alan Baldwin.)
