Salah's hat-trick lit up the game and gave Klopp's side the perfect boost ahead of next week's decisive Champions League meeting with Napoli.
And the manner in which the Egypt international took his goals -- in particular the two outstanding finishes for his second and third -- confirmed the forward is back to his best.
Bournemouth manager Howe put aside his disappointment at his side's heavy defeat to praise the Liverpool man.
"Salah looked very good today, his movement was very good, he looked razor-sharp," said Howe. "We did struggle to handle him, he's one of the best in the world."
And when Klopp was informed of Howe's comments, the Liverpool manager replied: "I think Eddie Howe is one of the best managers I have ever met so how could I say something different?"
Salah scored 44 goals last season and after an inconsistent start to the current campaign, has now struck 12 in all competitions.
"Whatever you do in a football game you need somebody to finish it off," said Klopp.
"And what Mo did around his two goals in the second half was just exceptional. I don't know in the moment a lot of players who would have scored these two goals.
"He was fouled for the first one but he wants to score the goals and stands on his feet and scores it. But the most impressive finish was his third goal. It was outstanding again, how he set it up, that was good."
Salah put Liverpool ahead in the 25th minute when he followed up Roberto Firmino's long-range shot to finish from 10 metres out.
He surpassed that early in the second half when he picked up a loose ball and ran from halfway, keeping going after an attempted trip by Steve Cook, before placing his shot inside Asmir Begovic's far post.
And the Egyptian completed his treble after a Cook own goal had killed off the game, again running from deep before this time twice rounding Begovic before placing the ball into the net.
Klopp said: "The whole game was brilliant from him (Salah) today -- not only the goals. He wanted to help with runs in behind and him scoring three goals is big for him and very important for us."
Victory moved Liverpool to the top of the table ahead of Manchester City's meeting with Chelsea but the Liverpool manager insisted his focus was now trained on the meeting with Napoli followed by the visit of Manchester United to Anfield next weekend.
"Today we can celebrate but then we have to recover and then prepare for Napoli," he said. "And that's how it is. But for today, all good."
Howe admitted his side missed Callum Wilson, the England striker who suffered a hamstring injury this week.
But while the Bournemouth manager was aggrieved an offside decision went against them for the opening goal, he conceded his side had been beaten by a team capable of sustaining their title challenge.
"We did miss Callum today -- he brings that unique mix of physicality and pace which would have troubled Liverpool’s backline maybe more than we did today," said Howe.
"Liverpool are very good. It is a very competitive league this year. I think it will go until the end. Manchester City, Liverpool and I think other teams will challenge too. It should be an entertaining end."