After dropping the first set, the British and Australian pairing hit back to register a 4-6 6-3 7-6 triumph.
The opening set saw both teams dominate on serve, but Matkowski and Zimonjic were able to put together an impressive four points to steal the solitary break of the set.
However, Murray and Peers responded at the start of the second, breaking the serve of their opponents before easing through the rest of the set.
The decider proved to be a tense affair, with the set progressing to a tie-break, which Murray and Peers dominated to create four match points.
However, the first two were saved by Matkowski and Zimonjic, but at the third time of asking, the eighth seeds got over the line as both players secured their first appearance in the last four at the US Open.