Goals from Bojan Krkic and Jonathan Walters subjected Tottenham to a fourth home defeat of the top-flight season, and Stoke's first league win over them since 2011.
Bojan's mazy dribble led to his first goal of the campaign in the opening six minutes, while Walters added a second just after the half hour with a close-range volley.
Pochettino's attempts to revive Tottenham after the break took time to have any effect, but eventually the hosts got back into the match as Nacer Chadli volleyed home from an improbable angle in the 78th minute.
Tottenham continued to push for an equaliser, but they were hampered by Kyle Naugton's late dismissal and Stoke's defence remained resolute to record a second league win away from home this term.
Victory lifts the visitors back into the top 10, while Tottenham's third league defeat in four matches sees them slip into the bottom half.
And the visitors took the lead two minutes later courtesy of Bojan's excellent solo effort.
Having exchanged passes with Steven N'Zonzi inside his own half, the former Barcelona striker embarked on a run towards goal from the halfway line and, with no Tottenham challenge forthcoming, he unleashed a low shot from 20 yards that beat Hugo Lloris.
Stoke's joy was dampened slightly in the seventh minute when Phil Bardsley, Mark Hughes' only change after serving a suspension, was forced off with a groin injury, Geoff Cameron replacing him.
Another defensive injury saw Stoke make their second change before the half hour as Marc Muniesa replaced Marc Wilson, but it failed to negatively impact the visitors who doubled their lead after 32 minutes.
Tottenham's defending was again poor, a simple Ryan Shawcross header finding Mame Biram Diouf in space and his square ball was tapped in by the unmarked Walters.
More disorganised defending from Tottenham almost gifted Stoke a third goal, as Federico Fazio gifted the ball to N'Zonzi inside the penalty area, but the Argentine's blushes were spared as the resulting shot was lashed wide.
With time running out Tottenham began to lay siege on the Stoke goal, Begovic saving brilliantly from a Lamela free-kick before Chadli finally reduced the deficit.
Tottenham's momentum was brought to an abrupt halt in the closing minutes as Naughton cynically brought down Victor Moses, and Stoke could have extended their lead further through substitute Stephen Ireland.
Lloris made a fine save to deny the midfielder and the final whistle was met by the sound of Tottenham's booing fans.
