The Seagulls were leading through Glenn Murray’s controversial penalty until a fluked effort from Mo Diame nine minutes from time hauled Newcastle level.
Then with a minute to go, substitute Ayoze Perez secured a 2-1 victory and lifted the Magpies back above Brighton at the summit.
Brighton went at their visitors from the start with Bruno and Sam Baldock forcing early saves from Karl Darlow.
The breakthrough came in the 14th minute when Ciaran Clark and Murray tangled in the area as they awaited a corner.
If anything the pair were wrestling each other, but top-flight ref Bobby Madley ruled in Murray’s favour and the striker coolly dispatched his 17th league goal of the season from the spot.
Newcastle equalised late on when Brighton keeper David Stockdale punched a corner to the feet of Atsu.
He mis-hit his shot completely on the edge of the area and it was hurtling yards wide.
However the ball spun off Diame and looped into the air, eluding Stockdale and finding the top right corner, leaving the goalkeeper crestfallen.
And there was an even later sting in the tail when Atsu got clear down the left and crossed for Perez to sidefoot a dramatic winner and put Newcastle back in control of the promotion race.
Elsewhere,Irish midfielder Conor Hourihane scored his first goal for Aston Villa as Steve Bruce’s men beat Bristol City 2-0. Jonathan Kodjia also netted for Villa.
Blackburn moved above Wigan with a 1-0 win over Derby.
A Craig Conway penalty proved decisive as Blackburn moved to 33 points, the same as 21st-placed Bristol City. But Rovers have a game in hand.
Stockdale, Saltor, Duffy, Dunk, Pocognoli (Tomori 18), Knockaert (March 88), Stephens, Sidwell, Murphy, Baldock (Kayal 82), Murray.
Darlow, Yedlin, Lascelles, Clark, Dummett, Atsu, Shelvey, Colback (Murphy 74), Ritchie, Diame, Gouffran (Perez 82).