Stoke defender Erik Pieters scored the decisive strike in the 42nd minute as his cross-come-shot drifted over Tim Krul and into the Magpies net.
We wanted to win because we’re trying to catch Newcastle
The Potters could have doubled their lead as Peter Crouch came close before Vurnon Anita wasted a late chance for the visitors.
Stoke are three points behind ninth-placed Newcastle following Saturday’s win, and Hughes challenged his Potters side to catch the Magpies.
“We’re pleased with what we’re producing at the moment,” Hughes told BBC Sport.
“We wanted to win because we’re trying to catch Newcastle. I felt the performance was good. We restricted Newcastle to few clear opportunities.”
Newcastle manager Alan Pardew refused to criticise his players despite the Magpies suffering a fourth straight league defeat.
“We just didn’t get the breaks. I can’t fault the character of the players and the honesty they showed,” Pardew said.
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