Parnaby played the first 45 minutes and Hines the whole game on a cold but dry afternoon which saw the visitors take the lead with only three minutes played when Alex Henshall swung over a left-wing corner and Alex Grant headed home.
Ryan Brobbel, impressive throughout, set about trying to get Boro back into the game and cut in from the left wing and crack in a right-footed shot which goalkeeper Daniel Bachmann saved at the second attempt.
Charlie Ward flashed a shot just off target as the visitors went for another which they nearly managed on the stroke of half time as Karim Rossi went for goal and a combination of Hines and Mark Kitching cleared.
When Andre Bennett, on for Parnaby at half-time, was brought down right on the edge of the penalty a few yards from the goal line Boro were in with a chance of putting pressure on the City rearguard but Bachmann did well to grab a low free-kick from Cameron Park.
Park just cleared the bar when set up by Brobbel a few minutes later, but Boro were handed a way back in the game, one they squandered, on 58 minutes. Ryan O'Reilly was adjudged to have handled a ball which had bounced awkwardly and Boro were awarded a penalty.
Bradley Fewster struck low, but Bachmann pulled off a terrific save away to his left.
An intuitive free-kick from Park almost caught out the goalkeeper but it landed in the side netting before Bachmann was finally beaten with 78 minutes played. Having blocked one shot, the City defence scrambled to try and clear but Wilson Kneeshaw turned sharply to strike home a low shot.
It took an excellent recovery clearance from Hines to deny James Alabi just a minute later, Birger Meling producing another soon after before Brobbel curled just over after nutmegging Adam Thomas and cutting in from the left.
Park curled just over from 22 yards as Boro went for a late winner, but that was to come from Stoke who struck in the 89th minute as Henshall cross low from the left inside the penalty area, Ward stabbed forward and James Alabi tapped home when virtually standing on the line.
Boro: Leutwiler; Parnaby (Bennett 46), Atkinson (capt.), Hines, Meling, Waters, Jones, Kitching, Fewster (Kneeshaw 60), Park, Brobbel. Unused subs: Fryer (gk); Weledji, B Halliday.
Stoke City: Bachmann; Wheeler, O'Reilly (Taylor 81), Ward, Grant, Watkins-Clark, Thomas, Lecygne, Alabi, Rossi, Henshall. Unused subs: Heneghan, Eve, Dawson, Richards.
Referee: Billy Khatib
Booking: Grant (Stoke), 59, dissent.
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