Sheffield United 2 Preston North End 2 - Match report as Lilywhites earn a draw right at the death
Stockley got his head to a corner from fellow substitute Paul Gallagher to level with the last action of an entertaining contest in South Yorkshire.
North End had fallen behind in the 36th minute to John Lundstram's low finish, before Daniel Johnson brought them level from the penalty spot nine minutes into the second half.
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Hide AdBut Billy Sharp's penalty at the other end just two minutes later saw the Blades regain the lead.
All credit to PNE, they kept on pushing for parity and got their reward with Stockley's goal, the final whistle sounding seconds later.
It was an encouraging performance from Alex Neil's side who should have opened the scoring when they hit the woodwork twice in a matter of seconds.
Scott Sinclair burst clear with a superb run from his own half, saw his shot come back off the post with Tom Barkhuizen putting the rebound against the same post.
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Hide AdNorth End lined-up 4-2-3-1, Barkhuizen operated as the central striker with Sinclair and Billy Bodin either side of him.
Daniel Johnson played the No.10 role, Ben Pearson and Ryan Ledson teamed-up further back in midfield.
There was a start for goalkeeper Mathew Hudson, presumably with Connor Ripley set to face Everton on Saturday afternoon in the continued absence of the injured Declan Rudd.
Both sides looked solid in the early stages with little created at either end in terms of chances.
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Hide AdGradually the contest started to come to life, Ben Osborn putting a header wide for the home side from Ollie Norwood's cross.
Bodin had the first decent sight of the Blades' goal, his low shot from 20 yards bringing a diving save from Wes Foderingham - the former Swindon goalkeeper who PNE put four goals past at Wembley in the 2014/15 League One play-off final.
North End should have gone in front in the 32nd minute following that stunning run from Sinclair.
Collecting a pass from skipper Johnson well inside his own half, Sinclair set off on a direct run down the middle of the pitch.
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Hide AdThe Blades defence parted and Sinclair found himself one-on-one with Foderingham, his shot from just inside the box coming back off the post and dropping into Barkhuizen's path to the right of goal.
Barkhuizen had plenty of the goal to aim at but managed to lift a shot against the outside of the same post Sinclair had hit.
Within four minutes, the home side took the lead at the other end.
Kean Bryan's cross from the left was headed clear by Patrick Bauer, the ball coming to Osborn whose pass in the pass was blocked by Pearson.
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Hide AdOli McBurnie got to the loose ball and laid it back into the path of Lundstram who stroked a left-foot finish across the box and into the far bottom corner of the net - Hudson only able to watch it go in.
The Premier League hosts were not far away from a second goal four minutes before half-time.
Bryan's low cross from the left channel was met at the near post by Osborn who back heeled it across the face of goal and just wide.
United made a double change at the interval. Lys Mousett and Regan Slater replacing McBurnie and goalscorer Lundstram.
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Hide AdWithin sixty seconds of the restart, Mousett was played clear of the North End defence but pulled a shot across Hudson and wide of the far post.
North End equalised in the 54th minute from the penalty spot, Barkhuizen having chased a ball over the top into the box.
Finding his route blocked by Phil Jagielka, Barkhuizen turned to try and get himself into a shooting position and got a push from Jack Robinson.
It was on the soft side but referee Jon Moss awarded a penalty and Johnson stroked it into the bottom corner.
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Hide AdLess than two minutes later Mr Moss pointed to the spot at the other end, the ball bouncing up against Pearson's hand as he tried to clear.
Sharp stepped-up to send Hudson the wrong way from 12 yards.
With the game getting stretched, North End could have equalised again in the 63rd minute as they counter-attacked their hosts.
Sinclair played Barkhuizen in down the left hand side of the box, Barkhuizen having a shot with the outside of his right foot which went straight into the gloves of Foderingham at the near post.
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Hide AdAt the other end, Norwood's free-kick from 20 yards beat the wall but was gathered cleanly by Hudson.
Soon after, an Osborn shot from the edge of the box crashed against angle of bar and post, hit Joe Rafferty on the lead and bounced into Hudson's gloves.
North End upped the pressure in the closing stages, Neil bringing on Stockley, Gallagher and Brad Potts with 10 minutes left.
Potts almost fashioned an equaliser with a low shot which Foderingham stuck out a foot to save by the post, before the other two subs combined for a 90th minute leveller.
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Hide AdGallagher delivered a corner from the left which Stockley headed home from inside the six-yard box.
United: Foderingham, Basham, Jagielka, Robinson, Baldock, Norwood, Lundstram (Slater 46), Osborn, Bryan, Sharp, McBurnie (Mousett 46, Hackford 72). Subs (not used): Verrips, Gordon, Graham, Brunt, Broadbent.
PNE: Hudson, Rafferty, Bauer, Davies, Hughes, Pearson, Ledson (Gallagher 80), Bodin, Johnson (Potts 80), Sinclair, Barkhuizen (Stockley 80). Subs (not used): Fisher, Earl, Bayliss, Harrop, Storey, Huntington, Ripley.
Referee: Jon Moss (West Yorkshire)