The final game, with Zverev serving at 5-3, was interrupted by shouts from an unruly fan who was tossed out by security.
The distraction ended a run of 14 consecutive points on serve, with the seed double-faulting once he was able to continue serving. He finished off the evening with a sharp volley winner at the net on his first match point.
Zverev completed his 40th win of the year in just over two and a half hours.
The world number three won the tournament in 2017 but had not been past the quarter-finals in Canada since.
“After losing the first set, I had to tell myself we were both playing well,” the holder of seven Masters trophies said.
“I had one or two mistakes at the end of the first, but it was a high-level match.
“I felt that if I kept playing well, I would get my chances – and I did. I can’t complain about the second and third sets.“
Zverev will bid for the oddly scheduled Thursday final against three-time semi-finalist Karen Khachanov, who dismissed young American Alex Michelsen 6-4, 7-6 (7/3).
“It was a very close, competitive match,” Khachanov said. “I had to come back from some tough situations.
“How you handle that mentally is important. I was glad to close it out in the second set.
“I had to try and not give him the opportunity to step in and attack; that’s what I did today.”
Zverev has won five of the seven matches he has played against Khachanov.
Popyrin and Zverev duelled throughout the evenly matched 71-minute opening set as it went into a tiebreaker.
Zverev was unable to convert on two winning chances, but Popyrin came good on his own second opportunity with a net cord winner that caught his opponent stranded at the baseline.
The German began to turn the tables in the second set, taking a 4-1 lead only to see the Aussie level at 4-all.
Zverev pulled away to level the match at a set apiece, breaking for 6-4 as Popyrin sent a volley wide.
The top seed began the final set with a 3-0 lead on his way into the tournament final four at the pre-US Open event.
Popyrin remains winless against Zverev after losing all four of their matches.
