Neither side was able to break the deadlock before the interval, despite Stoke having the better of the chances in the opening term.
Newcastle looked much more comfortable after the break, but it was the home side who eventually took the lead in the 80th minute courtesy of Xherdan Shaqiri's long-range strike.
The Potters went close to doubling their lead a short time later with Marko Arnautovic hitting the woodwork, before Jack Butland ensured Stoke kept all three points, with a stunning save from Seydou Doumbia's injury-time header.
Stoke were clearly the better side throughout the contest, dominating possession and territory. They struggled to create clear-cut goal-scoring opportunities in horrendous conditions however, until the class of former Inter Milan and Bayern Munich star Shaqiri shone through at the end.
Newcastle continued to struggle on the road this season, failing to add to their tally of seven goals in away matches – the worst record in the Premier League.
Stoke travel away to face Chelsea at Stamford Bridge on Saturday, while Newcastle host 15th-placed Bournemouth at St James' Park.
Well that feels bloody good, not many better feelings than winning a game like that! @XS_11official and the boys were brilliant #SCFC#JB1
— Jack Butland (@JackButland_One) March 2, 2016
400 @premierleague appearances and 3 points pic.twitter.com/Y1qM7PNxS3
— Peter Crouch (@petercrouch) March 2, 2016
Morning Stokies! Doesn't the morning after feel better after a victory? What a belter from this man #SCFCpic.twitter.com/zzraOaxGHJ
— Stoke City FC (@stokecity) March 3, 2016
"They were difficult conditions today. The first half went against us, but I thought we were excellent in getting hold of the ball and probing crosses. The negative was not getting on the end of them. Second half, with the wind, we thought it would be an advantage but it didn't turn out that way."
Newcastle boss Steve McClaren was happy with his side's effort, despite the result:
"I couldn't fault the players. We were organised, hard to beat, compact and we frustrated Stoke. They had one shot in the second half and scored. If we continue that hard work then we'll get what we deserve."
*Thanks to Opta
1 - Stoke have scored fewer goals from corners than any other Premier League team this season. Evolution.
— OptaJoe (@OptaJoe) March 2, 2016