The Mali international played for 82 minutes of a game in which a clinical second-half performance from the visitors earned them a deserved win, although the final margin of victory could have been greater but for an outstanding display by Potters goalkeeper Daniel Bachmann.
Sidibe, who was making a welcome return to action as he looks to bounce back from another long injury lay-off, had initially equalised Alex Pritchard's opener, before a quick-fire treble from Christian Ceballos, Ryan Mason and Andros Townsend put the game beyond Stoke's reach.
Fellow first-teamer Diego Arismendi joined Sidibe in the Potters starting line-up, while James Alabi continued up front after his impressive run of goal-scoring form.
Spurs' eleven had a strong feel about it, with fringe players Townsend, Jonathan Obika and Dean Parrett all afforded starts.
On five minutes, City had their first look at goal as Sidibe met Michael Clarkson's corner but his header flew over the bar.
They were made to regret the missed chance as, moments later, Spurs took the lead in very fortunate circumstances at the other end.
Lucas Dawson brought down Massimo Luongo 25 yards out, and Pritchard's deflected free-kick left Bachmann stranded as the ball floated into the net.
On eleven minutes, the visitors nearly doubled their lead when Ceballos' whipped free-kick was met by the head of Grant Hall, but his effort rebounded off the post.
After Townsend fired over moments later, it looked as though it was going to be a long afternoon for the Potters as Obika and then Ceballos forced excellent saves from Bachmann.
However, they grabbed an unexpected equaliser on 16 minutes through Sidibe - Jordan Richardson's inviting cross was met by the stretching forward, whose header nestled into the right-hand corner despite Jonathan Miles getting his hand to it.
Spurs continued to look threatening despite the setback of losing their lead, and after Ceballos had tricked his way through the Potters midfield, Obika drove his shot just wide of the post.
Stoke showed they dynamism in the final third on 20 minutes as a fluid move finished with Musungu winning the ball for Dawson, who crashed his shot against the post from 20 yards.
Tottenham pressed to re-establish their lead, and after Obika has fired a shot off the underside of the crossbar following a goalmouth scramble, Pritchard forced a smart stop from Bachmann at his near post.
The Potters were showing plenty of tenacity in their play, perhaps trying to exact revenge over the 7-2 thrashing they received from the same opponents earlier in the campaign, but Spurs had the game's next best chance.
Obika's shot was smothered by Bachmann after a delightful pass from Ceballos, before the striker once again tested the Austrian stopper's reactions with another low shot.
Six minutes before half-time, the two who combined for Stoke's goal did it again - Richardson's free-kick found Sidibe at the front post, but this time the striker mistimed his header and it cleared the target.
Soon after the break, Richardson forced an acrobatic stop from Miles after rasping a shot from 25 yards, although nothing came from the resultant corner.
However, it was Spurs who edged in front on 48 minutes - Townsend found a cross from the right hand side that picked out Parrett, and his reverse ball was clinically dispatched by Ceballos.
Parrett's deflected drive moments later produced another fine stop from Bachmann, with the Potters having a lot to thank for their stopper keeping them in with a shout in the game.
Luongo fired wide after another excellent Spurs move, and on 56 minutes the visitors were awarded a penalty after Ben Glasgow tripped Townsend in the area.
Mason, who grabbed a hat-trick when the two sides met earlier this season, sent Bachmann the wrong way to give his side the comfort of a two-goal cushion.
Townsend them got himself on the score-sheet three minutes later, as he cut inside to avoid the challenge of a City defender before finding the bottom corner via Bachmann's outstretched hand.
Richardson stung Miles' hands once more on 66 minutes, but Spurs were generally in control as they looked to turn a comfortable-looking victory into a rout.
In the 80th minute, Bachmann was once again equal to Spurs' advances as he kept out Luongo's downward header from Townsend's corner before beating away Pritchard's shot from the edge of the area.
He then saved from Ceballos and Townsend again as Spurs pushed for a fifth, but it didn't come as they had to settle for four.
Stoke City: Bachmann; Glasgow, Heneghan, Keane, Clarkson; Richardson, Dawson, Arismendi (Campbell 63); Musungu; Sidibe (Rossi 82), Alabi.
Tottenham Hotpsur: Miles; Fredericks, Hall (Stewart 62), Veljkovic; Luongo, Mason, Parrett; Townsend, Ceballos; Pritchard; Obika (Coulibaly 70).