It wasn’t a vintage performance by Liverpool at all, but there were glimmers of light from their dispatch AstonVilla and put your foot back on the accelerator in pursuit of the top four.

Mohamed Salah got the ball rolling, tying Kenny Dalglish’s goal for liverpool in almost double time before Virgil van Dijk increased Liverpool’s first-half advantage. Villa rightly responded through Ollie Watkins, but a calm finish from 18-year-old substitute Stefan Bajcetic for his first Liverpool goal left away support to shake their version of a Christmas classic. “Merry Christmas, Everton!” they sang in celebration.

Jürgen Klopp’s celebratory message to supporters touched on various themes, from his admiration for Love Actually to the ‘crazy world we live in at the moment’, and Liverpool’s Champions League final defeat in May – “Mr Courtois had a pretty good day” – to, more pertinently, move within “striking distance” of the top four. In an entertaining 37 minutes here they had reached fourth-placed Tottenham, who they are now five points behind with a game less.

This game was lively, sometimes so open it was silly, and sometimes slapstick, a kind of Wacky Races. Take, for example, the moment when Villa centre-back Ezri Konsa, facing his own goal, made a hash of a clearance that exploded into the sky. When the ball fell, Darwin Núñez, who was tireless but erratic in equal measure, took aim but his shot shot across his shin and harmlessly towards Robin Olsen, who replaced Emi Martínez, the Argentine keeper who had become the first Villa player to win. world Cup.

Klopp could only smile and shrug when asked what he thought of Trent Alexander-Arnold’s role in preparing for Salah’s opener. It came from Andy Robertson’s corner, which was cleared to Alexander-Arnold about 40 yards from Villa’s goal. The right-back allowed the ball to bounce, took a touch and used a bit of residual fizz to launch a delicious pass into Robertson’s path with the outside of his right boot. Robertson took the ball in his stride and rolled it into the goal with his first touch for Salah to hide.

Robertson’s clever thinking resulted in his 54th premier league assist, eclipsing Leighton Baines’ record for a defender. For Salah, it was his 172nd goal for Liverpool, on his 277th appearance. Dalglish reached that figure in 515 games. “When you’re mentioned in the same sentence as Sir Kenny Dalglish, you’ve done something right, so that’s a great moment,” Klopp said.

Alexander-Arnold was the subject of much discussion in the build-up to the World Cup, in which he played 33 minutes, and the England defender showed both sides of his game here. Liverpool hadn’t convinced defensively and on the looming hour, Villa were finally rewarded for their perseverance, even though they were trailing 2-0 at the time.

It seemed fitting that in a game riddled with errors, Villa’s goal came from yet another comedic clearance. This time, Alexander-Arnold inadvertently sabotaged the ball from one side of the pitch to the other. The ball landed at the feet of John McGinn and he located Douglas Luiz, who sent a curling cross into the box. Watkins launched between a flat-footed Alexander-Arnold and Joel Matip and headed into the far corner of Alisson’s goal. Klopp must have feared that would happen. Watkins had a strike early in the second half, also from a pass from Douglas Luiz, ruled offside.

Until then, Villa had their manager, Unai Emery, hopping and jumping on the touchline in frustration. Van Dijk had doubled Liverpool’s lead from another corner eight minutes before half-time and at the other end they were missing an edge. Watkins failed to generate enough power with a diving header moments after Leon Bailey made a painful mistake from inside the box.

“I want to be very optimistic and I’m disappointed, a bit angry, but I think the attitude of the players was amazing,” Emery said. “I want to be optimistic. We have to learn and add more things individually and tactically for the stage I want to do.

Liverpool never really felt the comfort of a two-goal buffer – their panic characterized by Alisson slipping on a clearance under little pressure – but they restored their advantage with nine minutes of regular time remaining on the clock. Núñez killed Joe Gomez’s flying pass with a superb first touch and fired a shot on goal, which Olsen parried. The ball fell to Bajcetic, who calmed down around the goalkeeper, slotted the ball between Tyrone Mings and recorded a moment he won’t soon forget.

When Núñez was taken off for Ben Doak, a 17-year-old who made his league debut with minutes to spare, there were high-fives all along the Liverpool bench. It was a satisfying return to business.