Hingis and Chan, formed this year after Chan parted ways with her longtime partner and sister Chan Hao-Ching, have dominated the circuit since forming and the second-seeded pairing did not drop a set in their six victories.
For Murray, the win brought the fifth major title of his doubles career.
It was tight all the way in the first to 10 points with Murray and Hingis prevailing to add the US Open title to the Wimbledon title they won in July.
A bid for a second slice of grand slam history has fallen short for New Zealand doubles specialist Michael Venus. She first quit in 2002 because of a long-term foot problem, returned at the start of 2006, but retired again in 2007 after testing positive for cocaine, which led to her being banned for two years. At the time, she denied taking the drug but did not appeal the ruling.
"It's been a lot of fun for me", Murray said.
Departure from Celtics 'still hurts' Thomas
That's it, Isaiah Thomas just declared war on the entire National Basketball Association and they better get ready to fight back. He didn't hold back in his message, and made sure to get one point across - that he doesn't hold a grudge: "I wasn't wronged".
The unseeded Stephens used her strong defensive skills to keep rallies alive, and Keys lost too many of them while making 17 unforced errors.
She said: "If I play, then definitely we will (play together)".
She won the 1997 US and Australian Open and Wimbledon singles titles and the 1998 and 1999 Australian Open singles crowns as well as seven mixed doubles titles, including this year's Wimbledon and US Open mixed titles.
Cori "CoCo" Gauff will try to become the youngest U.S. Open girls' champion on Sunday when she faces fellow American Amanda Anisimova.
"It's been a lot of fun for me and a great opportunity for me to compete with Martina".