After dropping the opening set, Murray and Soares hit back to level the match and looked to be the stronger pair until the Brazilian went 0-40 down on his serve at 4-5 in the third set.
However the third seeds won five points in a row to take the game and then broke themselves before Murray served out a 6-7, 6-2, 7-5 victory.
Jamie Murray falls in Madrid, Norrie loses Estoril final
It is the fifth time in the last nine grand slams that Murray and Soares have reached the last eight, but they have not gone further since winning their second slam title together at the US Open in 2016.
In the quarter-finals they will face 12th seeds Henri Kontinen and John Peers, Murray's former partner.
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