Liverpool hopes of securing a top four finish was under a threat at the Hawthorns stadium but the Reds dug deep to secure the maximum points.
Hal Robson-Kanu gave the host a shocking lead in the opening 15 minutes but Mohamed Salah pulled parity with his 22nd league goal of the season on the 33rd minute mark.
The game was poised to end in a 1-1 draw but goalkeeper Alisson Becker became Liverpool’s hero when he nodded home a cross from Trent Alexander-Arnold deep into injury time.
Speaking to the media after the game, Klopp, who was elated, said it was special for his side to win that way.
“Wow, is a pretty good word. It was spectacular and a good game. What a moment! That is so far the highlight.,” he told BBC Sport.
“I hope we have time for another highlight [this season]. It was a tricky game. Winning that way is really special. I couldn't be happier in the moment.
"It's the best goal I've ever seen scored by a goalkeeper! Strikers score like that. If Olivier Giroud scores like that you say it's a worldie. It's a worldie! Wow!
"[Alisson's] our player, our boy and our brother. When he is suffering we are all suffering. It's hard in these moments.
“There are more important things than football but when football can deliver moments like this for him, and all the boys, and our fans, then football is the best thing for a few seconds than anything else out there.
"We are not even halfway through. We have to win going to Turf Moor. We have to win. There will be a proper atmosphere and will not be a friendly game. West Brom fought really hard.
“I heard Sam Allardyce asked for professionalism before the game and he got that proper answer. In the situation we are in the only thing we have to do is keep pressure on our competitors around us. We recover and go again.
"I saw it plenty of times that players lose the plot [late on in games]. None of us did that. We were calm but full of desire.
“Three of the best chances we had were in the last five minutes. In these moments it was really good. It's not easy to stay calm in moments like this but we did and we got the rewards."
