Liverpool put their recent troubles behind them to comfortably beat Rangers 2-0 in the Champions League on Tuesday and move into second spot in Group A.
The win, thanks to a sumptuous first-half free kick from Trent Alexander-Arnold and a second-half penalty by Mohamed Salah, put the six-times European champions on six points after three games - three points behind leaders Napoli.
The Scots, who barely threatened Liverpool to the disappointment of their passionate fans complete with a bagpipe-player, remain bottom of the group on zero points.
In need of a morale booster after their poor start to the Premier League, Liverpool's four-man attack of Salah, Diogo Jota, Luis Diaz and Darwin Nunez swarmed over Rangers from the off.
Liverpool manager Jurgen Klopp was delighted by his team's tidy and confident performance, especially the first goal from Alexander-Arnold, who has come in for recent criticism.
Alexander-Arnold, whose chances of making England's World Cup squad are in the balance after recent below-par displays, struck a superb free kick over the wall and past Rangers goalkeeper Allan McGregor in the seventh minute to raise the roof off Anfield.
"The performance was great from the lads," said Alexander-Arnold. "No matter what, I always try to think positively. People say things but for me it's all about performing for the team. That's all that matters, getting wins and helping the team. It's been a slow start to the season for me but I'm looking forward to the rest of the season.
"We went back to a basic 4-4-2 and played it really well, shifted across the pitch well. We made it compact, they couldn't play through us, they were playing long balls and we picked them off.
"This year is going to be very intense. It's what we're used to, three games a week. There's no excuses. With the games coming thick and fast, it's exciting for us."
Nunez could have had a hat-trick in the first half as McGregor pulled off four saves in succession from the Uruguayan striker. But it was Salah who scored the second from the penalty spot in the 53rd minute after Diaz was brought down in the box.
The so-called "Battle of Britain" clash underlined the gulf in quality between the top flight divisions in England and Scotland.
Rangers looked drained and exhausted trying to stem Liverpool's attacks as the intuitive Thiago Alcantara blocked attacks and fed through balls from midfield.
Virgil van Dijk, who has been in the firing line for Liverpool's leaky defence of late, was barely troubled at the back, although Rangers substitute Rabbi Matondo did force a goal line clearance from Kostas Tsimikas in the dying minutes.
