City went close to pulling the game back with Michael Okeke striking the woodwork but Lowe added a second for the visitors.
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And City started strongly, going close inside five minutes when Jaden Heskey seized on an underhit backpass, taking it around the keeper before flashing an effort across goal.
Emilio Lawrence then forced the first save of the game with a driven effort from the edge of the box and Harrison dragged an effort just off-target after a neat work from Michael Okeke.
City keeper George Murray-Jones made two smart saves from close range before Lowe finally swept home at the third attempt.
The quick double rocked City and Lowe went close to a second before we re-established control of the game with Ashton Muir going close to an equaliser following a driving run from Okeke.
Lowe was a constant threat on the break, and he forced another good save from Murray-Jones before he beat the City keeper after racing clear again.
City kept pushing and came close to puling a goal back when Okeke found space in the box but his low shot smacked against the foot of the post and Stoke saw out the victory.
