A long ball forward led to a terrible mix-up at the back between Fabricio Coloccini and Harper, who fluffed his clearance and allowed Green to chip the ball over his head.
The Championship leaders were quick to respond and Posh keeper Joe Lewis twice denied Nolan before the midfielder levelled.
Jose Enrique raced down the left and picked out the former Bolton star, who managed to divert the ball into the bottom corner with his back to goal.
Three minutes after the break, Ameobi was fouled 25 yards from goal and Barton nonchalantly curled the ball over the wall and past Lewis for his first goal since October 2008.
Ameobi then powered a header wide from a fine Barton cross, before he gave the visitors a two-goal cushion.
Leon Best passed into Ameobi's feet on the edge of the area and he turned away from his marker before firing a low shot which Lewis got a hand to but could not keep out.
Best twice came close to finding a fourth but it was Posh who set up an exciting finale when Exodus Geohaghon launched a huge throw into the middle and Dickinson forced the ball home at the back post.
However, Posh were not able to snatch a result and their stay in the Championship looks set to end.
Meanwhile, the apparent formality of Newcastle's promotion can be sealed in front of their home fans on Easter Monday night when Sheffield United visit St James's Park.
Peterborough manager Jim Gannon on the possible appointment of Gary Johnson as his replacement: "Gary is a manager with a fantastic CV and I believe it would be an excellent move to appoint him.
"That decision is out of my hands, but I have given my advice to the club.
"Should a new manager come in before the end of the season, I will happily stand aside."
Newcastle manager Chris Hughton: "We are so very close and hopefully we can finish the job at St James's Park on Easter Monday.
"That would be an excellent reward for the supporters who have backed us so fantastically all season.
"We want to wrap up promotion at the first opportunity and while that didn't happen today, we are nearly there."
Live text and stats
Saturday, 3 April 2010
05 Zakuani yellow card
06 Lee (Bennett 55)
22 Torres (Simpson 46)
25 Green (Mackail-Smith 46)
03 Jose Enrique
07 Barton (Gutierrez 87 yellow card)
21 Pancrate (Routledge 46)
20 Best yellow card
23 Ameobi (Butt 83)
Ref: HaywoodAtt: 12,877
Attempts on target
Attempts off target
90:00+4:55 The final whistle goes and the game is over.
90:00+2:51 Lee Frecklington restarts play with the free kick.
90:00+2:51 Booking Booking for Jonas Gutierrez.
90:00+2:37 Free kick awarded for a foul by Jonas Gutierrez on Tommy Rowe.
88:51 The assistant referee signals for offside against Kevin Nolan. Joe Lewis takes the free kick.
88:06 Direct free kick taken by Joe Lewis.
88:06 Booking Booking for Leon Best.
88:00 Jonas Gutierrez gives away a free kick for an unfair challenge on Kerrea Gilbert.
86:29 Substitution Jonas Gutierrez replaces Joey Barton.
85:45 Corner taken by Tommy Rowe from the left by-line to the near post, Header from deep inside the penalty area by Liam Dickinson
goes harmlessly over the crossbar.
83:53 Nicky Butt gives away a free kick for an unfair challenge on Lee Frecklington. Free kick crossed left-footed by Tommy Rowe.
82:25 Substitution Nicky Butt on for Shola Ameobi.
80:59 Alan Smith gives away a free kick for an unfair challenge on Josh Simpson. Lee Frecklington takes the direct free kick.
80:10 Liam Dickinson produces a cross, Headed effort from deep inside the penalty area by Lee Frecklington goes harmlessly over
79:03 Scott Griffiths concedes a free kick for a foul on Wayne Routledge. A cross is delivered by Wayne Routledge, Shola Ameobi
takes a shot. Save by Joe Lewis.
77:59 The assistant referee flags for offside against Craig Mackail-Smith. Free kick taken by Steve Harper.
75:31 GOAL - Liam Dickinson:Peterborough 2 - 3 Newcastle Liam Dickinson grabs a goal from close range low into the middle of the goal. Peterborough 2-3 Newcastle.
74:48 Corner taken by Lee Frecklington from the right by-line to the near post, clearance by Sanchez Jose Enrique.
74:36 Lee Frecklington takes a shot. Blocked by Joey Barton.
72:04 Joey Barton challenges Tommy Rowe unfairly and gives away a free kick. The free kick is swung in right-footed by Lee Frecklington.
71:11 Scott Griffiths sends in a cross, Fabricio Coloccini makes a clearance.
68:29 Corner from right by-line taken by Joey Barton.
66:10 Unfair challenge on Wayne Routledge by Tommy Rowe results in a free kick. Alan Smith takes the free kick.
65:20 The ball is sent over by Wayne Routledge, Leon Best has an effort at goal.
64:38 Corner taken by Joey Barton from the right by-line, clearance made by Liam Dickinson.
64:23 Leon Best takes a shot. Save by Joe Lewis.
64:05 Centre by Wayne Routledge, clearance by Gabriel Zakuani.
63:47 Craig Mackail-Smith is caught offside. Mike Williamson takes the free kick.
60:42 The ball is sent over by Scott Griffiths, Danny Simpson gets a block in.
58:44 The assist for the goal came from Leon Best.
58:44 GOAL - Shola Ameobi:Peterborough 1 - 3 Newcastle Shola Ameobi finds the net with a goal from long range to the bottom left corner of the goal. Peterborough 1-3 Newcastle.
57:19 Leon Best has an effort at goal from the edge of the box that misses to the right of the target.
56:45 Effort on goal by Tommy Rowe from long distance goes over the crossbar.
56:07 Danny Simpson produces a cross, save by Joe Lewis.
54:41 Substitution Ryan Bennett comes on in place of Charlie Lee.
54:03 Danny Simpson sends in a cross.
53:11 The official flags Josh Simpson offside. Steve Harper takes the free kick.
52:14 Centre by Lee Frecklington, Steve Harper makes a save.
51:42 Leon Best takes a shot. Blocked by Gabriel Zakuani.
51:03 A cross is delivered by Wayne Routledge, Joe Lewis makes a save.
50:02 Joey Barton produces a cross, Shola Ameobi produces a header from the edge of the box and misses to the right of the target.
49:50 The ball is swung over by Joey Barton, Gabriel Zakuani makes a clearance.
49:00 The official flags Craig Mackail-Smith offside. Steve Harper takes the free kick.
47:48 GOAL - Joey Barton:Peterborough 1 - 2 Newcastle Joey Barton hits the back of the net with a goal direct from the free kick from outside the penalty box to the top left corner
of the goal. Peterborough 1-2 Newcastle.
46:41 Booking The referee books Gabriel Zakuani for unsporting behaviour.
46:37 Foul by Gabriel Zakuani on Shola Ameobi, free kick awarded.
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