Liverpool crushed Southampton 4-0 on Saturday to put pressure on Premier League leaders Chelsea as Arsenal got back on track with victory over Newcastle to hand Eddie Howe his first defeat as Magpies manager.
Steven Gerrard made it two wins out of two as Aston Villa boss with a 2-1 win at Crystal Palace while the matches between Norwich and Wolves and Brighton and Leeds both ended goalless.
Liverpool's third consecutive victory in all competitions since losing at West Ham lifted them to second in the table, one point behind Chelsea, who host Manchester United on Sunday.
Third-placed Manchester City would go move back into second place if they beat West Ham, also on Sunday.
Free-scoring Liverpool have now scored 39 goals in their 13 Premier League games this season, their highest goal total at this stage of a top-flight campaign, and Klopp welcomed their return to top form.
"We didn't only lose at West Ham, we drew two games before as well," said Klopp. "So, all of a sudden, we were in a bad moment. Now we look like we are in a better moment."
He added: "The things that happened to this team in the last few years were special and that's mostly because of the outstanding mindset and mentality of the boys."
Jota netted again in the 32nd minute with a simple finish from Mohamed Salah's pass for his eighth club goal this term.
Thiago Alcantara had ended a lengthy goal drought in the midweek Champions League win over Porto and the Spain midfielder was back on the scoresheet in the 37th minute before Virgil van Dijk bagged Liverpool's fourth shortly after half-time.
- Arsenal back to winning ways -
Arsenal's 10-match unbeaten run in all competitions come to a painful end in last weekend's 4-0 thrashing at Liverpool.
But second-half goals from Bukayo Saka and Gabriel Martinelli at the Emirates Stadium made it four wins from their past five league games with a 2-0 success over Newcastle.
Written off after their poor start to the season, Mikel Arteta's side are fifth, level on points with fourth-placed West Ham, as they chase a berth in next season's Champions League.
Howe was in charge of Newcastle in person for the first time after missing last weekend's 3-3 draw against Brentford following a positive coronavirus test.
While the Saudi-led consortium that recently bought Newcastle have spoken about emulating the success of Manchester City under Middle Eastern ownership, Howe's only focus is saving the Magpies from relegation.
The former Bournemouth boss will need to drag much-improved performances from his winless team if they are to avoid a catastrophic slide into the Championship.
Already languishing six points from safety, bottom-of-the-table Newcastle face crucial games against fellow strugglers Norwich and Burnley over the coming week.
"Momentum in football is so important," said Howe. "We need to get that win as quickly as we can.
"I'm a positive guy. I've seen enough from the two games to see we can compete. A neutral watching today wouldn't think we were in the position we were in. It's up to us to get the results we need."
Gerrard earned his second successive win since taking charge of Villa as the former Rangers boss masterminded a victory at Crystal Palace, courtesy of goals from Matt Targett and John McGinn.
Dean Smith, the man Gerrard replaced at Villa, remains unbeaten as Norwich boss after the second-bottom Canaries drew 0-0 with Wolves at Carrow Road.
Brighton drew 0-0 with struggling Leeds in Saturday's late match, with Seagulls manager Graham Potter ruing his team's lack of killer instinct.