Cenk Tosun dealt a blow to Stoke's Premier League survival hopes as he scored twice in Everton's 2-1 win at a snowy Bet365 Stadium.
The Potters played an hour with 10 men after Charlie Adam was sent off by Martin Atkinson for a foul on Wayne Rooney.
They fell behind to Tosun's opener (69) from close range after his initial header had been saved, but Stoke had substitute Eric Choupo-Moting to thank for their leveller when he side-footed in Joe Allen's excellent free-kick - injuring himself in the process, and lasting only six minutes in total before he was forced back off.
Tosun's diving header then finished off Theo Walcott's cross with six minutes to go, leaving Stoke three points from safety having played a game more than many of their relegation rivals.
On a day of changing weather in Staffordshire, with snow blizzards and clear sunshine interchanging at will, the main talking point before the break came thanks to Atkinson.
His decision to send off Adam appeared harsh. The Scotsman and Rooney were competing for a 50/50 ball on the edge of the Everton box and Adam's challenge was late rather than dangerous.
Everton could not press their man advantage before the break as Stoke held firm in increasingly difficult conditions, but finally did so when they produced the first move worthy of a goal all afternoon.
Yannick Bolasie's cross was headed goalwards by Tosun, and at the second attempt he turned the ball in for the opener despite Ryan Shawcross' best efforts.
Everton looked more likely to double their advantage than the deflated Potters did to find an equaliser, but they pulled level when Choupo-Moting, brought on four minutes earlier, popped up at the far post to slot home Allen's brilliant free-kick from deep.
All of a sudden, the hosts looked confident - but it was shortlived, as Walcott's inviting cross was turned in by Tosun with a low header Butland perhaps should have saved, to leave Stoke's route to survival as treacherous as the weather at the Bet365 Stadium.
What's next?
Stoke's tough time at the bottom doesn't get any easier, with a trip to the Emirates Stadium to face Arsenal on April 1.
Everton have a home game with Manchester City on March 31 with Liverpool coming up at Goodison Park seven days later.