He will play either the second seed Roger Federer or the unseeded Korean Hyeon Chung in Sunday's final.
Cilic won the US Open in 2014 and lost to Federer in the final at Wimbledon last July. The 29-year-old's greater experience in high profile encounters was evident as he broke Edmund to lead 4-2. He plundered the Briton's serve again to claim the opener after 35 minutes.
The second set was more evenly contested as Edmund recovered the poise that took him past the likes of 11th seed Kevin Anderson and the third seed Grigor Dimitrov.
"I think in the second set I was a bit up and down with my game and not getting enough returns back," said Cilic. "He started to serve quite good. I stayed mentally very focused and tried to play every single point. It was crucial in the tiebreak to keep that pressure."
The Croatian took it seven points to four. And with Edmund tiring with the toll of matches, the third set became a stroll.
"I noticed in the third game of the third set, when I broke him, he just let a couple of balls go past him," added Cilic.
"So I realised his movement was a little bit restricted, so I just tried to move the ball around and obviously that second break was extremely crucial."