Mykhailo Mudryk scored a sensational solo goal as Chelsea kept alive slender hopes of qualifying for Europe via the Premier League with a 3-2 win over Newcastle at Stamford Bridge.

At 2-1 late in the second half, the result was in the balance but it was tipped decisively in Chelsea’s favour by a moment of magic from the substitute, taking the ball off Conor Gallagher’s foot at top speed and bamboozling his way beyond defender Fabian Schar before rounding the goalkeeper and finishing.

The win marked a significant step forward for Mauricio Pochettino’s side, who have so often allowed balanced duels – as this undoubtedly was – to slip away from them.

Nicolas Jackson gave them a sixth-minute lead with a smart backheeled goal from Cole Palmer’s shot, before Alexander Isak rifled Newcastle level at the end of the half.

Palmer got his 13th of the season to restore the lead, a brilliant, driven finish from range.

Mudryk’s goal with 15 minutes to go looked to have settled it before Jacob Murphy made Chelsea think with a superb 90th-minute strike, but the hosts hung on for a deserved win.

Struggling in 11th, they had needed all the aid they could muster, and were promptly handed a boost by Newcastle defender Sven Botman after six minutes.

Malo Gusto’s low cross was well pitched but should have been an easy mop-up job for Botman. Instead, he carelessly swept the ball to the right boot of Palmer, whose tame shot from outside the box was intelligently flicked home via the deftest backheeled touch from Jackson.

Raheem Sterling looked determined that a strong start should not go to waste, muscling beyond Tino Livramento down the left and offloading to Jackson to strike low at goal, this time easily saved by Martin Dubravka.

Yet the one-goal lead was fragile, and Chelsea were exposed when Trevoh Chalobah headed a weak clearance straight to Anthony Gordon who shot wide.

Isak was inches from connecting with Murphy’s cross as it zipped across the face of goal, then skied over from two yards out as the ball came back in, comfortably the visitors’ clearest chance of the half so far.

European qualification through the league is still not beyond Chelsea. Victory here would take them to within four points of seventh-place West Ham with a game in hand, but consistency has been this team’s downfall under Pochettino.

In the final minutes of the half, they allowed Newcastle back in. The hitherto impressive Gusto was caught trying to juggle the ball in midfield. Chalobah raced up to take charge, but he was dispossessed by Bruno Guimaraes and was caught horribly out of position.

The ball broke to Isak, who skipped inside the box and curled an exquisite shot around Axel Disasi and beyond the dive of Djordje Petrovic.

Chelsea might still have led at the break had Sterling’s driven 18-yard effort been hit either side of Dubravka. In truth though, 1-1 was a fair conclusion to a balanced half.

Sterling came close again at the start of the second period, bursting into the box and lashing a shot narrowly wide at the near post.

Chelsea were looking the more confident side on the ball, penning Newcastle inside their own half, and they retook the lead on 57 minutes.

Enzo Fernandez collected the ball centrally and fed it in to Palmer, receiving with his back to goal 20 yards out. The home side’s top scorer took one touch to turn inside and then crashed it with his left foot inside Dubravka’s near post.

Sterling should have put it beyond doubt minutes later, carrying the ball around the goalkeeper but denied on the line by Dan Burn who was covering.

There were a few nerve-jangling moments as the visitors tested Chelsea’s defence with balls into the box that were cleared not wholly convincingly.

Then came a moment of magic from Mudryk and, despite Murphy’s late rocket, at last a glimmer of a happy ending to a turbulent season.