Hingis won the US Open mixed title with India's Leander Paes in 2015 while Murray was a mixed champion with Jelena Jankovic at Wimbledon 10 years ago.
"We've played a lot of good tennis this week and I think three times here we've won 10-8 so it just shows how fine the margins are in mixed doubles with the format we play".
Now Murray and Hingis will be looking to build on their success at Wimbledon earlier this year.
But it was Hingis' class that made the difference, as she hit two backhands up the line on match point, setting up Murray for the winning volley. I got broken [at 4-3 in the second set] and said: "'Maybe it's really time to play now.' He did great", Hingis told the tournament Web site.
She'll go for No. 25 in women's doubles on Sunday - with Chan's sister as her partner. "Hopefully we play more". "She's such a great player, a huge champion of the game", he said.
The Swiss teamed up with Jamie Murray of Great Britain to reach the mixed doubles final on Friday, defeating CoCo Vandeweghe and Horia Tecau, 6-4, 7-6 (8).
In the fifth game of the second set Murray held his serve from 0-40 down and played superbly in the next game, winning successive points with a stunning half-volley and then a backhand return victor down the line as Vandeweghe was broken for the second time.
Rojer wore a shirt showing a picture of the Statue of Liberty in what he said was a message about peace and freedom in the aftermath of last month's violence at a rally of neo-Nazis and white nationalists in Charlottseville, Virginia.