For Andoni Iraola, at the end of a week of vexation following two avoidable one-goal defeats, this was just what the doctor ordered. On a cool November day, a comfortable margin of victory in second gear in South London halted Liverpool’s two-game losing run heading into the internationals and catapulted them back into the top-four, nine points off leaders Arsenal.

Even Florian Wirtz, Liverpool’s ultimate attacking fall guy over the last 15 months or so, netted a much-needed first Premier League goal of the season. Off a Bradley Barcola assist, too. Here at Selhurst, amid a forward quartet made up of just shy of £400m worth of transfer fees, there were more positive sprinklings of encouragement. And when Alexander Isak, who it should be said is second in the race for the golden boot with seven league goals, smashed the ball home on the cusp of 90 minutes, the three points were safe and heading back up to the north-west.

That said, this was all against a Crystal Palace side – and a manager in beleaguered Frenchman Pierre Sage – who by the end looked out of ideas and inspiration. No head coach has lost his job in the Premier League this season – yet – but the Eagles are now rooted to the bottom of the table after 10 games with just two wins to their name. Could a change be in the offing from Palace chairman Steve Parish, a man who does tend to afford managers time to put things right? We’ll find out soon enough.

Yet what will frustrate Sage the most on this occasion is that, until Liverpool’s second just after half-time, Palace were well in this match. Yet the team that has scored the second-fewest goals in the division (nine) were punished here for failing to take their chances in the first-half.

But a week on from failing to have a single shot on target against Arsenal, it took 20 seconds for Liverpool to find their range here as Mac Allister gave Dean Henderson an early test. The diminutive 5’9” midfielder, curiously effective from set pieces, went closer after 10 minutes, heading into the side netting from Dominik Szoboszlai’s free-kick. It was a warning and routine that Palace would not heed.

Yet after the first 15 minutes, Palace were the team on the ascendancy. Yeremy Pino’s neat swivel and shot crashed off the crossbar while Jogen Strand Larsen, in for the suspended Jean-Philippe Mateta, saw a dinked finish ruled out for offside, albeit correctly so.

And when Daichi Kamada gave Barcola a lesson in back-post volleys with a punchy effort kept out by Alisson, it was somewhat against the run of play when Mac Allister’s opener arrived.

Iraola had spoken in the build-up about his team perhaps being “too honest” as a statistic this week did the rounds: while Liverpool have conceded the most fouls in the Premier League, only three sides have won fewer fouls. But it pays to be shrewd: after Cody Gakpo won a questionably-given foul off Jefferson Lerma, Szoboszlai’s near-post free-kick was once again met by Mac Allister, who glanced sweetly home for his fifth goal of the season, equalling his tally from the last campaign.

His provocative celebration in front of the Holmesdale End only added to the home crowd's fury. “One-nil to the referee,” they sang at the interval.

Yet the Reds were fortunate to be ahead at half-time. Their goal was under siege before the interval, with Quinten Timber and Adam Wharton forcing good saves out of Alisson. Palace’s momentum was stymied by the break though and when Barcola’s square ball after a surge down the right found Wirtz, the German found the attribute he so often has been accused of lacking since his £105m arrival on these shores: composure. Stroking the ball beyond Henderson, it is just his sixth Premier League goal since arriving from Bayer Leverkusen last summer.

But even in the closing stages, Palace carved out decent opportunities. Mino somehow squandered a one-on-one opportunity with the goal gaping and substitute Eddie Nketiah poked over from close range. It was indicative of Palace’s fortunes: neat build-up, a large intake of breath in the box before failing to find the back of the net.

And when Isak put the icing on the cake, set up by Wirtz in the box and coolly cutting inside before lashing home past Henderson, Sage had the look of a man on the brink on the touchline. Even Milos Kerkez’s brainless foul on Dario Osorio in stoppage time, clattering the Palace substitute’s head in the box, which resulted in Nketiah’s consolation penalty, could not brighten the mood. Now, ahead of a two-week pause in action, the question for Parish is: will he stick or twist?