This was not a vintage Liverpool performance by any stretch but there were glimmers of sparkle as they dispatched Aston Villa and put their foot back on the accelerator in pursuit of the top four. Mohamed Salah got the ball rolling, equalling Kenny Dalglish’s goalscoring mark for Liverpool in almost double-quick time before Virgil van Dijk increased Liverpool’s first-half advantage. Villa deservedly replied through Ollie Watkins but a composed finish by the 18-year-old substitute Stefan Bajcetic for his first Liverpool goal left the away support rattling through their version of a Christmas classic. “Merry Christmas, Everton!” they sang in celebration. Jürgen Klopp’s festive message to supporters touched on various themes, from his admiration for Love Actually to the “crazy world we are living in at the moment”, and from Liverpool’s Champions League final defeat in May – “Mr Courtois had a pretty good day” – to, most pertinently, moving to “within punching distance” of the top four. Within 37 entertaining minutes here, they had homed in on fourth-placed Tottenham, whom they are now five points behind with a game in hand. This game was lively, sometimes so open it was silly and, occasionally, slapstick, a Wacky Races of sorts. Take, for example, the moment when the Villa centre-back Ezri Konsa, facing his own goal, made a hash of a clearance that rocketed into the sky. When the ball dropped Darwin Núñez, who was tireless but erratic by the same measure, took aim but his shot cannoned off his shin and harmlessly towards Robin Olsen, who deputised for Emi Martínez, the Argentina goalkeeper who had become the first Villa player to win the World Cup. Klopp could only grin and shrug his shoulders when asked for his thoughts on Trent Alexander-Arnold’s role in the buildup to Salah’s opener. It stemmed from Andy Robertson’s corner, which was cleared as far as Alexander-Arnold about 40 yards from the Villa goal. The right-back allowed the ball to bounce, took a touch and used a bit of residue fizz to ping a delicious pass into the path of Robertson with the outside of his right boot. Robertson took the ball in his stride and rolled it across goal with his first touch for the lurking Salah to tap in. Robertson’s smart thinking resulted in his 54th Premier League assist, eclipsing Leighton Baines’s record for a defender. For Salah, it was his 172nd Liverpool goal, in his 277th appearance. Dalglish reached that figure in 515 games. “When you are mentioned in the same sentence as Sir Kenny Dalglish then you did something right so it’s a big moment,” Klopp said. Alexander-Arnold was the subject of much debate in the buildup to the World Cup, in which he played 33 minutes, and the England defender exhibited both sides of his game here. Liverpool had not convinced defensively and with the hour mark looming Villa were eventually rewarded for their persistence, albeit they were 2-0 down by then. It seemed apt that in an error-strewn game the Villa goal came from another comedic clearance. This time Alexander-Arnold inadvertently hoofed the ball from one side of the pitch to the other. The ball landed at John McGinn’s feet and he located Douglas Luiz, who sent a curling cross into the box. Watkins launched himself in between a flat-footed Alexander-Arnold and Joël Matip and steered his header into the far corner of Alisson’s goal. Klopp must have feared it was coming. Watkins had had an early second-half strike, also from a Douglas Luiz pass, ruled offside. Until then Villa had their manager, Unai Emery, hopping and skipping 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 lacked a cutting edge. Watkins failed to generate enough power with a diving header moments after Leon Bailey painfully miscued from inside the box. “I want to be very optimistic and I am disappointed, a little bit angry, but I think the attitude was amazing from the players,” Emery said. “I want to be optimistic. We have to learn and add more things individually and tactically for the step up I want to do.” Liverpool never really felt the comfort of a two-goal buffer – their panic typified by Alisson swiping at a clearance under little pressure – but they restored their advantage with nine minutes of normal time left on the clock. Núñez killed Joe Gomez’s flighted pass with a superb first touch and skittled a shot at goal, which Olsen parried. The ball fell for Bajcetic, who calmly shimmied around the goalkeeper, tucked the ball between Tyrone Mings and recorded a moment he will not forget in a hurry. When Núñez was withdrawn for Ben Doak, a 17-year-old given his league debut with a couple of minutes to spare, there were high-fives all round on the Liverpool bench. It was a satisfying return to business.