Jonathan Walters had put Stoke 1-0 up heading into the interval on Saturday, but quickfire strikes from substitutes Philippe Coutinho and Roberto Firmino turned the Premier League game on its head.
However, Klopp insisted that his side are indebted to Mignolet, who - after denying Charlie Adam earlier on - produced a stunning save to prevent Saido Berahino tucking in a maiden Stoke goal late on.
"Simon Mignolet, what a save. The second was spectacular but both are good," a jubilant Klopp told BBC Sport.
"I have no idea how. That was genius and I am really happy for him. He saved our life."
"The second half was really good but we played a big gamble bringing on Firmino and Coutinho," Klopp added. "Phil [Coutinho] lost three kilos in the last three days.
"The first half was not the players, it was the way we play football. It was obvious that Stoke were better tuned but they didn't create a lot of chances, other than the goal.
"But, it's job done, it feels good. Nice weather, 63 points and I couldn't feel any better."
18 - Liverpool have won more points from losing positions than any other Premier League team this season (18). Recovery.— OptaJoe (@OptaJoe) April 8, 2017
Stoke manager Mark Hughes, on the other hand, was left to rue missed opportunities - and mistakes defensively - by his side, who have now lost their last four league games.
"We needed to take our chances and capitalise when we were on top," the Welshman told BBC Sport.
"I was happy, we were good value at 1-0 and restricted them to very little. They brought their big hitters on which made an impact but it took a mistake from us.
"It was a long ball down the middle and we should have dealt with it. When those are the things that are happening you think maybe it's not your day.
"We've come through a tough period of fixtures. Now we need to get the job done and make sure we get more points on the board quickly."