Harry Maguire celebrated his second goal in two games as if it was a cup-final victor.
Arnautovic, Saido Berahino and Shaqiri continued to cause Hull problems but Stoke were nearly punished for failing to take their chances, Oumar Niasse unable to get what would have been a decisive touch on Sam Clucas' flick on from Lazar Markovic's cross. Mark Hughes assured everyone there was no sense of panic after four straight defeats, though there must have been a degree of concern when Hull came back from a goal down and began looking for a victor in the second half.
But the Switzerland global teed up Marko Arnautovic for Stoke's opener in Saturday's contest and, after Peter Crouch had restored the hosts' lead following Harry Maguire's leveller, it was Shaqiri who put the game to bed in stunning fashion.
Hull have won four of their last five league games at the KCOM stadium but have not won away since August, and Elmohamady believes the club's home form remains vital for their survival hopes. If they continue playing as enterprisingly as this they have a decent chance. "We need to pick up points away to stay in the Premier League".
The Tigers started the second half well and were deservedly level when Maguire bundled a deflected shot into the back of the net after the home side failed to clear a corner. Michael dawson was then beaten easily by Arnautovic, who while holding off Harry Maguire, thumped a shot into the net off the underside of the bar.
"People now are coming to Hull knowing it's going to be hard for them". Burnley then came close to a leveller but Kamil Grosicki and Oumar Niasse were denied by Lee Grant and Martins Indi respectively.
Hughes's response was to send on the tried and trusted.
Goalkeeper Eldin Jakupovic then rescued Hull with a terrific stop from a header by substitute Jonathan Walters and Niasse, on loan from Everton, was then again wasteful as he wildly blasted over with the goal at his mercy.
Shaqiri scored a wonder goal to settle the match after that though. Perhaps Andrew Robertson could have been a little quicker in closing him down, though there is not much anyone can do about a magic left foot. Jakupovic had no chance.
Mark Hughes' second-half substitutions pay dividends - A section of Stoke fans have become increasingly frustrated with the Welshman after a horrendous run of results but even the harshest critic has to take their hat off to the Potters' boss today. It's a fantastic goal.