The Brazil international glanced in Trent Alexander-Arnold’s stoppage-time corner to clinch a dramatic 2-1 victory.
He became just the sixth goalkeeper to score in the Premier League after Peter Schmeichel, Brad Friedel, Paul Robinson, Tim Howard and Asmir Begovic.
Liverpool’s constant second-half pressure looked like counting for nothing after Mohamed Salah cancelled out Hal Robson-Kanu’s opener before the break.
Klopp said: “If Olivier Giroud is scoring that everyone says it’s a world-class goal, with Alisson doing it we have to say the same.
“We created chances and it needed to come in the last second. What a goal, what a worldie and unbelievable goal, the technique was insane.
“It couldn’t have been a better moment, it’s just perfect for today. If he is never doing it again I’m fine, it’s a perfect moment.
“We didn’t have a lot of moments in this season so we shouldn’t take it for granted. My part of the goal is I didn’t shout to stay back.
“He went there and what a goal, it’s incredible we have already seen it 10 times back in the dressing room.
“He’s a wonderful person, funny, smart, thoughtful and intense in moments. He is just a great guy. It couldn’t have been for a better person after what he went through (losing his father).”
Albion took the lead after 15 minutes when Robson-Kanu wriggled onto Matheus Pereira’s pass to score his first top-flight goal since November 2017.
Salah levelled 18 minutes later as Albion were caught out by a quick free-kick after referee Mike Dean ordered a restart when he obstructed Fabinho.
Firmino hit the post two minutes later and Mane had a goal disallowed for offside soon after the break.
Liverpool’s pressure was relentless but they escaped with 20 minutes left when Kyle Bartley had a goal ruled out with Matt Phillips adjudged to be offside and interfering with play.
Yet, just as it looked like the Reds’ top-four hopes were virtually over, Alisson came up to glance in Alexander-Arnold’s corner from six yards.