The victory ensures that Liverpool will face Chelsea in the final at Wembley on Feb. 27.
With the two sides playing out a 0-0 draw at Anfield in the first leg, there was everything to play for between the Gunners and the Reds.
The odds were stacked against Mikel Arteta's side who had conceded 43 goals in 16 games across all competitions against Liverpool since Klopp took control. However, the home side started the brighter. Bukayo Saka won an early free kick after just outside the box and Alexandre Lacazette hit the post with his shot.
Liverpool had few chances to get high up the pitch in the first half but took their chances when they did. They had a goal ruled out on 13 minutes when Joel Matip was judged to be offside when he headed the ball past Aaron Ramsdale.
It didn't take long for Liverpool to secure the lead, though, with Jota given too much space by the Arsenal defence on 19 minutes. He was able to find himself an angle and bobble the ball into the net from just outside the penalty box.
The home side appeared to lose their grip on the match as the half wore on with their initially impressive press slowly receding. Lacazette had a golden chance to equal the sides early in the first half but, with just Caoimhin Kelleher to beat, he sent his shot high and over the bar.
Liverpool nearly doubled their lead on the hour mark when Trent Alexander-Arnold delivered a cross into the box.
Ibrahima Konate's header hit the woodwork before Ramsdale scrambled to save Jordan Henderson's rebound shot. It was early goalscorer Jota, however, that eventually gave Liverpool their second after a lengthy VAR review.
He got the better of Ben White and chipped the ball over Ramsdale on 77 minutes to secure Liverpool's win. The goals mark Jota's fifth and sixth against Arsenal in all competitions since he joined Liverpool.
Arsenal were reduced to 10 men on 89 minutes when substitute Thomas Partey -- who had just returned from Africa Cup of Nations duty earlier in the day -- received a second yellow card within three minutes of his first. He had only come on on 74 minutes as a substitute for Emile Smith-Rowe.
Klopp was quick to praise Jota and his goal-scoring prowess afterward.
"Quality is why we signed him because of the way he played at Wolves," Klopp said after the match. "The defending he had to do, the runs he had to make but was still able to produce some exciting stuff. "He didn't only just step up tonight. Yes he scored two goals but he is incredibly important for us.
"The mix of his skillset is incredibly exciting."
Arteta was left to rue the loss after the strong start to the match.
"It is disappointing because obviously when you have the final one game away you have that excitement," Arteta said at a news conference after the game. "We did everything we could to put out a competitive team.
"They [Liverpool] have the quality to finish the game off.
"You need to have a squad of 22, 23 top outfield players and to do that, it takes time."