It was a decision that might have cost Swansea when Shaqiri was bundled over in the box by Fernandez - but Arnautovic's spot-kick was wild.
Hull remain two points above Swansea in 17th place after beating Watford 2-0, but Clement feels the momentum has shifted back towards his side.
Casual play at the back nearly cost Stoke early on, but Bruno Martins Indi recovered to prevent Gylfi Sigurdsson cutting the ball back to Llorente in the six-yard box.
The hosts began brightly and were ahead after just 10 minutes, Gylfi Sigurdsson's corner falling neatly to the unmarked Fernando Llorente, who leapt up and headed past returning goalkeeper Jack Butland.
Sigurdsson has now provided a league-high seven assists from set-plays this season and created 44 chances from dead-ball situations.
Carroll nearly scored a second as Swansea carved Stoke open, but Stoke keeper Jack Butland, making his first appearance after a year out with an ankle injury, pulled off an acrobatic save to deny him.
However, the Stoke fans will hope the team can end the campaign strongly, with a top-half finish firmly in the Bet365 Stadium outfit's reach.
Here's All of Collider's Star Wars Celebration Orlando Coverage
We also have confirmation that we'll be fighting on Yavin-4, Starkiller Base, and Tatooine at some point. The franchise's next film, Star Wars: The Last Jedi is scheduled to premiere on December 15, 2017.
Stoke manager Mark Hughes bemoaned Marko Arnautovic's missed second-half penalty as the turning point.
As Swansea pushed on for a third, so Butland was forced to pull off a wonderful save from another long range effort from the increasing influential Carroll.
Speaking on BBC's Match of the Day, former Chelsea midfielder Frank Lampard singled him out following another lacklustre display from relegation-threatened Swansea that extended their winless run to six games.
- Only Kevin De Bruyne (13) has more Premier League assists than Gyfli Sigurdsson this season (12 - level with Eriksen), while the Icelandic worldwide has provided more from set plays than any other player in the competition (7). Away from Britannia, Stoke have won just three games so far this season.
"But they scored from their first corner".
Alfie Mawson was signed in the summer by the Swansea and has been a regular starter under Paul Clement, playing the full 90 minutes in the Swans' last 19 league games.
- New Alleged Photos Of Moto X (2017) Leaked
- United misses deadline to answer senators on dragging
- National Hockey League roundup: Maple Leafs in playoffs for first time since '13
- Patriots open 7-point favorites over Chiefs for Week 1
- Microsoft commits to major Windows feature releases twice a year
- York police arrest over 100 men in child prostitution investigation
- Ontario housing measures aimed at renters, buyers
- Fleeing With Student, Teacher Took Guns, Cash and Wife's Car
- Married man sends hijack hoax email to avoid trip with girlfriend
- Mnuchin says will unveil tax reform plan 'very soon'