The 23-year-old came off the bench to fire the hosts to their first opening-day victory since 2009.
Michael O'Neill's Potters were twice pegged back in an entertaining encounter at the Bet365 as Nick Powell and Jacob Brown's efforts were cancelled out by John Swift and Liam Moore.
But Surridge secured a welcome three points as fans returned to the ground for the first time in 18 months.
Over 19,000 spectators were in attendance and they were treated to a set-piece masterclass from former Bosnia and Herzegovina international Mario Vrancic.
Stoke stopper Josef Bursik produced a stunning early save to Andy Rinomhota's effort from a tight angle in the 13th minute.
An exciting three-minute first-half burst saw the game spring into life as Stoke went 2-1 up in the blink of an eye.
Tommy Smith expertly found Powell at the back post to poke home his perfectly-weighted free-kick in the 25th minute.
But the Royals immediately hit back.
Swift quickly equalised as he took advantage of some lapse defending to fire home.
However, the hosts went down the other end to bag their second.
Powell turned provider for former Barnsley striker Brown to nutmeg Reading keeper Rafael Cabral.
Defender Danny Baath could have made it three when he headed over Vrancic's corner on the half-hour mark.
Another Vrancic corner caused panic in the visitor's box as Powell nodded off target.
Playing from the back almost cost O'Neill's side on the stroke of half-time as Lucas Joao missed the target from 25 yards after Bursik's clearance.
Stoke missed a glorious chance to double their lead with the last kick before the break when Ben Wilmot steered Baath's header wide.
Vrancic picked up from where he left off as Scotland international Stephen Fletcher headed over another wicked delivery.
Reading stopper Cabral has his palms stung by a well-struck Morgan Fox volley.
The drinks break, which was booed by both sets of supporters in the 57th minute, worked wonders for Veljko Paunovic's outfit.
Moore pulled the visitors level on the hour as he powerfully headed Swift's corner beyond Bursik.
Down the other end, Josh Tymon blasted over the bar as Stoke searched for a third lead.
Surridge almost made an instant impact after coming on as he forced Cabral into a fine stop.
Brown frustratingly fired over the bar after being played in by Vrancic.
But Surridge made no mistake with just four minutes left as his deflected effort evaded Cabral after Vrancic's clever dummy.