North End looked like they had turned things round when goals from Luke Foster and Stuart Beavon gave them a lead going into the five minutes added on time, but Baker and Clarke ended the Lilywhites' dreams of a trip to the Final.
The home took the lead four minutes before the interval, when Steven Jennings flicked the ball in at the back post from Leon Clarke’s knockdown.
However, Foster headed his frst goal for the Club and then Beavon saw a deflected effort put North End 2-1 ahead, only for the late drama to send The Sky Blues into the Area Final.
North End lines up with a three-pronged frontline, with Holmes joining Beavon and Garner in attack and it was the former Derby winger who had the first effort of the game on five minutes, driving a shot in that the Sky Blues’ defence was able to get behind.
Steve Simonsen was into the game early and he did well to gather at the feet of former North End loanee Clarke after a quick break.
Clarke and McSheffrey were the main threats for the home side and the latter drilled a right foot effort just wide of the left hand post on 13 minutes.
North End had a massive shout for a penalty at the midway point of the half as Joel Byrom’s shot appeared to have been blocked by the arm of Jordan Clarke, TV pictures seeming to back up North End’s shouts.
On 37 minutes Leon Clarke was threaded through by McSheffrey, in a left hand channel, but hit shot went wide right. On the break debutant Joe Garner - at the other end – picked up the ball from a quick throw by Lee Holmes, ran in and drove shot just against outside of post and into side-netting.
The deadlock was broken on 41 minutes. A free kick was delivered into the box by Carl Baker, headed down by William Edjenguele and Steven Jennings in at the back post beat Steve Simonsen to it and clipped it over him from two yards out.
On 57 minutes, shortly after the introduction of Jeffrey Monakana, John Welsh won a corner with a driving run and deflected shot and Nicky Wroe did the same just past the hour mark.
On 66 minutes Joe Garner was smashed in the box with another big penalty shout, which eventually led to a corner and from that Lee Holmes inswinger Luke Foster rose highest to power home an equaliser at the front post.
A great save by Simonsen on 77 minutes denied McSheffrey from a left hand channel. But a free kick 25 yards out gave the home side a chance with McSheffrey and Baker over it, the latter hit it and clipped the top of the right corner of the bar.
But on 80 minutes North End went in front. Jeffrey Monakana had the ball on the right, but fed Stuart Beavon and he drifted in on his left foot before unleashing a left foot effort that deflected off Wood and flat-footed Murphy before ending in the back of the net.
The last few minutes were difficult for North End with Steve Simonsen clearly having pulled a muscle, but North End having used all their substitutes. The No.23 was forced to hobble on as five minutes of stoppage time was added on.
And the home side were able to draw level in the second minute of it as Carl Baker drilled home at the near post after the ball had been thrown into the box.
And within 45 seconds they were ahead as a shot came in and back out off Steve Simonsen and Leon Clarke was on hand to slam home from only a couple of yards out to end North End's hopes of Wembley.
PNE line-up: Simonsen, King, Buchanan, Byrom (Monakana, 56), Cansdell-Sherriff (Robertson, 18), Foster, Wroe, Welsh, Garner, Beavon (Procter, 82), Holmes. Subs not used: Stuckmann, Beardsley.
Coventry City line-up: Murphy, J Clarke, Baker, Fleck, McSheffrey (Elliott, 86), Jennings (Moussa, 75), L Clarke, Wood, Edjenguele, Bailey (Thomas, 53), Adams. Subs not used: Dunn, Cameron.
Referee: Mr R Madley
Attendance: 12,655 (485 away fans)