The American, seeded third at the US Open warm-up event, saw off Belgium's Goffin 7-6(5) 6-3 to book his place in the last four and keep alive his hopes of defending the title he won last year.
"I was pressing a little bit in that first set," said Isner, who hails from nearby Greensboro. "I was waiting for him to lose the set or make a mistake on a big point rather than me going after the ball.
"But I was happy with the way I played in the tiebreaker, and I played much better in the second set."
Tsonga, the top seed, sent sixth seed Marcel Granollers of Spain packing with a comfortable 6-1 6-2 victory which the Frenchman completed in just 53 minutes.
"I played well," Tsonga said. "I was into the match from the beginning and played good tennis. I don't know if he played his best tennis, I think he was a bit injured. But I played good tennis."
In the other semi-final, second seed Tomas Berdych will meet Sam Querrey.
Second seed Berdych was the first player into the semis after he came from behind to beat Steve Darcis 4-6 6-2 6-0.
The Czech came through strongly after a disappointing start against his Belgian opponent.
Berdych dropped serve twice in the opener, with Darcis doing enough to take the set.
But after the initial setback, Berdych won 53 of the next 80 points to race to victory.
"He was playing really smart, so I needed to change something," Berdych said. "I stepped a little bit closer to the baseline, and started to hit the ball a little faster. It changed the whole rhythm."
Awaiting the Czech in the next round is seventh seed Querrey, who edged Alexandr Dolgopolov of Ukraine 7-5 4-6 7-6(3).
Dolgopolov proved a tough customer for Querrey though, and the fourth seed took the match all the way to a deciding tie-break in the third set.
"It seemed that things just changed dramatically in the tiebreaker," said Querrey. "It feels good to get the win today, but the matches are going to get tougher. I'm just going to have to play better if I want to keep winning."