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Britain's Murray and Switzerland's Hingis won 6-4 6-4 in one hour four minutes on Centre Court.
Both Murray and Hingis are bidding for their second Wimbledon mixed doubles titles.
Britain's Heather Watson and Finland's Henri Kontinen, who won the title last year, are also into the last four.
They progressed via a 6-7 (4-7) 6-4 7-5 win over India's Rohan Bopanna and Canada's Gabriela Dabrowski and will play the second-seeded pair, Brazilian Bruno Soares and Russian Elena Vesnina, in the semi-finals.
Kontinen is hoping to pick up his third Grand Slam title after winning the Australian Open doubles in January alongside John Peers.
Murray, who lifted the SW19 mixed doubles title in 2007 alongside Serbia's Jelena Jankovic, and Hingis, who won it in 2015 with Indian Leander Paes, will play the Spanish-Brazilian combination of Maria Martinez Sanchez and Marcelo Demoliner.
The pair only announced their partnership last week and again looked comfortable as a partnership on the court.
Hingis has won five mixed doubles titles at Grand Slams as well as 12 women's doubles and five singles competitions - including Wimbledon in 1997.
Murray won men's doubles titles at the Australian Open and US Open last year with Brazil's Bruno Soares.
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Jamie Murray and Martina Hingis beat British pair Ken Skupski and Jocelyn Rae to reach the Wimbledon mixed doubles semi-finals.