Perez hit a two-run homer in the fifth inning, topping Bench's total from 1970 for the most by a player who played at least 75% of his team's games at catcher.
"It was unbelievable,'' he said. "I thank God for this. It's amazing.''
Perez also moved into a tie for the major league lead in homers with Toronto's Vladimir Guerrero Jr. and leads the majors with 115 RBIs, the first catcher with that many RBIs since Mike Piazza in 1999.
It has been a long road for Perez this season to put himself in contention for the home run title. He trailed Shohei Ohtani -- the home run leader at the time -- by 12 at the All-Star break and made up the distance by hitting 25 homers since July 24.
Only Jimmie Foxx in 1935 has won the home run title after trailing the leader by at least 12 dingers at the All-Star break, according to research by ESPN Stats & Information.
"I had never hit 30 in my career,'' Perez said. "So I was looking for 30 homers and 100 RBIs. This is a dream come true.''
Perez's career high in home runs was 27, which came in both the 2017 and 2018 seasons. Being in the same company with Bench is something else special for the 31-year-old Perez who has been a mainstay for the Royals since reaching the majors in 2011.
"When you see a Hall of Fame catcher, you try to be just like him," Perez said. "I'm going to try my best to be one of those guys.''
Starting again behind the plate -- the durable All-Star has seen some time at designated hitter -- Perez drove a 1-2 pitch from Triston McKenzie into the left-field bleachers, a drive that traveled 429 feet. Perez pointed to the sky after crossing home plate and was hugged by several teammates as he entered the dugout.
"For a guy who's so respected in this clubhouse, it was different than your normal home run,'' Royals manager Mike Matheny said. "You could see the look on Salvy's face. He'll never forget it.''
Perez tied Bench on Thursday night in Kansas City as the Royals played Seattle. He went 1-for-13 at the plate in the final three games of the series but didn't feel any pressure to set the record and was more focused on winning games.
"Perez is one of those rare individuals to find energy and passion just to keep playing,'' Indians interim manager DeMarlo Hale said. "And the offensive year he's having it's even more special. People don't talk about him in the MVP race, but I'll tell you what, he's there in my book.''
Perez also singled in the first and made his presence known defensively when he threw out Myles Straw trying to steal second base in the bottom of the inning.
"He's a great hitter, to start,'' McKenzie said. "Second of all, he's a great catcher. Threw out Straw early in the game, kind of shut down some of our momentum. He's a guy that can always make you pay for mistakes. He did just that. He has definitely caught fire toward the end of the season.''
Information from The Associated Press was used in this story.