Word of Ricardo Pereira’s winner for Leicester against Manchester City spread like an electric pulse through Anfield. Liverpool were coasting at the time against Newcastle but now the entire stadium became charged, standing as one and singing with greater conviction about winning the league. With more justification too. Liverpool believe.

The 100th victory of Jürgen Klopp’s Liverpool reign moved his team six points clear of Tottenham at the top of the table, seven clear of City, and extended their unbeaten run at Anfield to 30 league games. On current form, which is improving from a position of strength, they will take some stopping in the second half of the season. Dejan Lovren, a controversial Mohamed Salah penalty, Xherdan Shaqiri and the substitute Fabinho spread the goals through a team that is clicking at precisely the same moment as the reigning champions falter.

“I thought that was because of us,” said Klopp of the moment Anfield rippled with excitement over a goal at Leicester. “I’m really naive. I thought: ‘That is really nice, thank you very much’. Then I heard after the game it was about another result! Obviously nobody told our crowd that Tottenham won 5-0. It is fine. The atmosphere for Boxing Day was really good and exceptional in that moment but I thought it was because of us.”

His team’s efforts, quality and superiority over Newcastle did not go unheralded, however. Klopp refused to join in the euphoric reaction to City’s latest defeat – at least not in public – and described a six-point lead on Boxing Day as merely an encouraging platform. Rafael Benítez was more forthcoming on the possibility of Liverpool claiming the crown that eluded him at Anfield. “They are good enough to win the title, yes,” the Newcastle manager said. “They have a very good team and a very good squad with good players on the bench. If you want to win a league title you have to be consistent and they can do it.”

Liverpool’s perfect Boxing Day began with a present from Jamaal Lascelles, the Newcastle captain, who made a mess of a straightforward clearance, teed up Lovren for his first goal of the season and undermined his team’s encouraging start in one action. There was no pressure on the central defender when Andy Robertson whipped over a cross from Shaqiri’s short corner but he miscued a header back across the area. The ball dropped invitingly for Lovren who swept an emphatic, rising drive into the roof of Martin Dubravka’s net. It was a finish that would have found approval from the onlooking Kenny Dalglish, Kevin Keegan and Alan Shearer, though not the defending obviously.

Mohamed Salah was awarded a controversial penalty by referee Graham Scott. Photograph: Lee Smith/Action Images via Reuters

Benítez’s team had started brightly with their threat from set pieces and Matt Ritchie’s deliveries stretching Liverpool. Unfortunately for the visitors it was not only Lascelles who struggled with his heading. Joselu, starting ahead of Salomón Rondón as Benítez selected with Saturday’s trip to Watford in mind, could have put Newcastle ahead when Ritchie’s cross sailed over Virgil van Dijk. Unmarked in the six-yard box, the Spanish striker headed down and several yards wide of Alisson’s goal.

Liverpool were in no mood to offer further invitations once in front, however, and controlled proceedings. Sadio Mané was close to converting Roberto Firmino’s through ball only for Dubravka to save well with his feet. The Newcastle keeper was also alert to a powerful free-kick from Shaqiri that took a slight deflection off Mohamed Diamé before being beaten from a highly controversial penalty moments after the restart.

Salah converted the spot-kick low to Dubravka’s right having won it with a theatrical tumble as he cut into the area from Trent Alexander-Arnold’s pass. Paul Dummett touched the Liverpool forward’s arm but not enough to impede Salah or produce the collapse that followed. Graham Scott, the referee, bought it and Liverpool scored a Premier League penalty at Anfield for the first time since November 2016. Benítez called it “a soft penalty that changed everything” but the legitimacy and merit of Liverpool’s victory was never in question.

With the threat from Newcastle nonexistent Klopp could afford to look ahead and rest Georginio Wijnaldum and Firmino for the remainder of the contest. Shaqiri converted the third after the visitors failed to clear a dangerous low cross from the fit-again Alexander-Arnold. Jordan Henderson threaded a fine ball back to the defender on the right and, from his second attempt, the Switzerland international was on hand to beat Dubravka convincingly from close range.

Anfield was still digesting the news of Leicester’s second against City when Fabinho headed home Salah’s corner at the near post – his first Liverpool goal – with Diamé slow to react. Alisson preserved his clean sheet with a fine late save from the debutant Sean Longstaff and Liverpool moved serenely on, and six points clear, at the Premier League summit.