Paul Clement described the penalties that started and completed Everton’s comeback as “clumsy” but it was a touch of class that kept Swansea City rooted to the foot of the Premier League. Gylfi Sigurdsson provided it and, barring a recovery akin to Sam Allardyce’s work at Goodison Park, his former club will ultimately pay a much higher price than the £45m they banked for the Iceland international in the summer.

The league’s bottom club were in control for almost 45 minutes at Everton but one needless foul in the penalty area by Roque Mesa on Aaron Lennon changed everything. Dominic Calvert-Lewin equalised Leroy Fer’s opening goal after Wayne Rooney’s spot-kick had been saved on the stroke of half-time.

Thereafter, and without truly impressing, Everton eased to victory. A successful Rooney penalty embellished the margin of victory but Sigurdsson’s fourth goal of the season, swept superbly beyond Lukasz Fabianski from 25 yards, was the key to Allardyce’s return of 10 points from a possible 12 as Everton manager.

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“Gylfi was always going to get better and better,” said Allardyce, who has overseen and benefited from a major improvement from Everton’s record signing. “I was speaking to Paul before the game and he was saying the transfer knackered them up and knackered Gylfi up because it took so long so that when he arrived he wasn’t match fit. Now he has got to the level of match fitness we are seeing the best of Gylfi. His own professionalism and his own responsibility is part of that too. The Iceland lads are very proud of where they come from and of playing in the Premier League, I’ve managed a few, and he wants to prove he is worth every penny we paid for him.”

Swansea may have been backed into a corner over Sigurdsson’s transfer and recouped a tidy sum but they are paying the price for his absence. Clement’s side arrived on foggy Merseyside having scored nine league goals all season, the lowest return in England’s top four divisions and as many as Rooney alone had plundered for their opponents.

Their prospects of reaching double figures appeared even more remote when Wilfried Bony hobbled off after only five minutes and one touch of the ball. Bony’s absence with a hamstring injury was keenly felt earlier in the campaign and they can ill afford a repeat, yet their initial response was encouraging for Clement.

Facebook Twitter Pinterest Wayne Rooney scores with a second-half penalty after missing from the spot in the first half. Photograph: Gareth Copley/Getty Images

Luciano Narsingh and Bony’s replacement, Tammy Abraham, had the pace and alertness to punish a languid Everton performance in the first half. Allardyce’s pre-match warning about complacency proved prescient and the home side were extremely fortunate to go in level at half-time.

Swansea deservedly took their Premier League goals tally into double figures when Fer converted Tom Carroll’s corner beyond an exposed Jordan Pickford. Carroll’s delivery from the right eluded a mass of red and blue shirts at the near post. Fer, arriving unmarked behind the bunch, scored with ease from close range.

The visitors were in control only to give it away when Lennon raced on to Rooney’s flick in first-half stoppage time and was sent tumbling by Mesa’s needless challenge. Clement had no complaints over Jon Moss’s decision. Rooney’s spot-kick was superbly tipped on to a post by Fabianski but the rebound fell perfectly for Calvert-Lewin, who swept the ball past the unfortunate Swansea goalkeeper.

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Everton’s continued slow tempo in the second half prompted the introduction of Tom Davies for Morgan Schneiderlin and their performance improved almost immediately. Within moments of his introduction the young midfielder picked out Rooney in space and he swept the ball out to Sigurdsson on the left.

The former Swansea favourite cut inside Kyle Naughton before bending an unstoppable shot around Fabianski and inside the far post. Sigurdsson’s celebrations were restrained while his team-mates revelled in a moment that illuminated an otherwise subdued night.

From toiling and trailing, Everton ended the contest comfortably in the ascendency. Swansea’s display, in stark contrast, never regained the spark or threat of the first half. Their meek acceptance of defeat will be a grave concern for Clement. The game was put beyond them by a second penalty, this time awarded for a clip by Martin Olsson on Jonjoe Kenny’s heel as the right-back raced into the box. Replays were inconclusive as to whether the offence occurred outside the area or on the line.

There was no disputing Rooney’s finish. He went the opposite way to the first spot-kick, so did Fabianski, but the keeper was powerless to prevent the former England captain converting Everton’s seventh penalty award of the season.