Peterborough briefly led through Dominic Green but Kevin Nolan's 14th goal of the season hauled Chris Hughton's side level before the break.
A fine Joey Barton free-kick and a third goal from Shola Ameobi secured the points which leaves the Magpies with one foot back in the Premier League.
A single point from their remaining six games will rubber-stamp the promotion but their vastly superior goal difference means that Magpies fans can start planning for a return to Old Trafford, Stamford Bridge and Anfield next season.
Peterborough's inevitable relegation will wait until Monday but they made a game of their fifth defeat in a row thanks to Liam Dickinson's late header.
Jim Gannon's side may be two divisions below Newcastle in August but they made a bright start, with Green stinging the palms of Steve Harper from 25 yards in the opening minute.
Newcastle controlled the possession for the next few minutes, with Nolan and Barton impressive, but they fell behind in the 11th minute thanks to Green's opportunist goal.
A long ball forward led to a terrible mix-up at the back as Fabricio Coloccini and Harper left it to each other.
Harper fluffed his clearance and Green lofted the ball over his head and into the back of the net with his weaker right foot.
Posh could have doubled their lead moments later when Tommy Rowe flicked the ball into the path of Sergio Torres, but as Harper came out to narrow the angle the midfielder lobbed the ball wide.
The leaders were quick to respond, however, and could have drawn level midway through the half.
The Magpies moved the ball quickly through midfield and when the ball fell at the feet of captain Nolan inside the area a goal looked on the cards, but Posh keeper Joe Lewis pulled off a fine reflex save to tip the ball away.
Nolan then powered a header in from Fabrice Pancrate's cross but was again denied by Lewis before he finally found the net in stoppage time at the end of the first half.
Jose Enrique surged clear down the left and picked out the midfielder with his back to goal in the box and he managed to divert it beyond Lewis and into the bottom corner.
The impetus was all with Newcastle and it took just three minutes of the second period for Hughton's side to take the lead.
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 powered a header wide from a fine Barton cross as the visitors turned the screw before he made it 3-1 in the 59th minute.
Leon Best passed into Ameobi's feet on the edge of the area and he turned away from his marker and lashed in a low shot which Lewis got a hand to but could not prevent from finding the back of the net.
Best twice came close to finding a fourth but it was Posh who found the net next thanks to Dickinson's 76th-minute header.
Exodus Geohaghon launched a huge throw into the middle and after Nolan had inadvertently helped the ball on Dickinson forced it in at the back post.