Paul Clement admitted luck was on his Swansea team’s side as goals from Fernando Llorente and Tom Carroll ensured they ended a six-game winless run. It has given the Liberty Stadium faithful hope that the Welsh team can pull off another great escape.

Their previous successful rescue mission came in 2003 when a 4-2 win over their current relegation rivals Hull stopped the Swans from falling out of the Football League. History could repeat itself, but this time by ensuring they extend their six-year stay in England’s top tier.

Hull’s unlikely win over Watford, where they played with 10 men for over an hour, means 18th-placed Swansea are still two points adrift of a safe position. However, their gutsy display proves they are up for the fight. The two-point gap could have been extended if Marko Arnautovic had converted his second-half penalty to draw Stoke level. His miss came seconds before Carroll doubled the lead.

“It’s the first time I’ve called it a must-win game and I was right because if Hull had won and we hadn’t, the gap at five points would have been very difficult for us,” Clement said. “We created lots of chances and had a little bit of luck with the penalty miss. We haven’t had most things go our way but that little moment did. The momentum is with us. Hopefully it will give us that impetus to finish really strongly. We’re right behind Hull, breathing down their necks.

“We were strong, aggressive and physical. I’m happy with the way we used the ball. It takes a lot of bottle to do that in a high-pressured game.”

Clement’s bold tactics paid off in a game he said was the club’s biggest since the Championship play-off final in 2011. The former Real Madrid and Bayern Munich assistant moved star man Gylfi Sigurdsson into his preferred No10 position in a new-look 4-4-2 diamond formation.

Swansea pestered Stoke’s rearguard and were rewarded when their top goalscorer Llorente headed them in front in the 10th minute. The Spaniard connected with Sigurdsson’s corner and directed his header past Stoke goalkeeper Jack Butland, who was making his first Premier League start since fracturing his ankle in March 2016.

Llorente’s 12th goal of the season came at the perfect time after the former Juventus striker had been criticised by Match of the Day pundit Frank Lampard for his lacklustre performance against Watford last weekend. Sigurdsson underlined his value once again. He has scored or assisted 20 of their 39 Premier League goals this term. Even if they avoid relegation, Swansea will find it difficult to keep the £35m-rated Iceland playmaker at the Liberty Stadium in the summer.

Saido Berahino spurned two golden opportunities to not only draw Stoke level, but score his first goal in red and white colours since his £12m move from West Brom in January.

The former Swansea midfielder Joe Allen’s pinpoint cross found an unmarked Berahino, who somehow headed wide. He then failed to find the net again when he headed straight at Lukasz Fabianski from five yards, seconds before the break.

The visitors started the second half with more purpose. Federico Fernández had to be at his best to block Arnautovic’s goal-bound strike.

But Fernández would go from hero to zero when his trip on Xherdan Shaqiri inside the box gave Stoke the chance to equalise from the spot on 69 minutes. Arnautovic stepped up and blazed his penalty over the bar.

Just seconds later Swansea went up the other end and doubled their lead thanks to Carroll’s 25-yard strike, which took a mean deflection off Allen to beat Butland. Stoke could have lost by a larger margin if Butland had not denied Carroll and Jordan Ayew late on. Swansea then defended valiantly and this much-needed win keeps them in touching distance of survival.

Stoke are chasing a fourth successive top-10 finish under Mark Hughes but will have to improve on their dreadful away form if they are to do so.. They have lost eight of their last 10 away games.

“I was disappointed with how we started the game because we talked about that beforehand and wanted to affect Swansea,” said Hughes. “But unfortunately we didn’t and they scored with their first corner . The match-defining moment was the penalty and it needed to go in from our point of view. We missed it and they went down the other end and scored from a deflected shot.”