The 12th-ranked American came through 6-3, 7-6(11) and will face Germany's Jan-Lennard Struff for the title on Sunday in what will be his seventh tour final.
"I have played some solid tennis. It is one of my favourite surfaces. It is good to get out here and get some matches," said Tiafoe who saved six set points in a marathon second-set tie-break.
Third-seeded Tiafoe is chasing his third tour-level title and second of the season this week, having triumphed on clay in Houston in April.
Struff saw off Polish fourth seed Hubert Hurkacz 3-6, 6-3, 6-3 to close in on a first-ever title.
The 33-year-old cracked 35 winners past Hurkacz in his 89-minute victory.
"I am very happy," Struff said. "Hubi is an incredible grass-court player, so I knew I had to play a very good match. After starting off well I found a way and I am very happy with the win."
