The Cobbles looked to have completed a dream double of Premier League scalps as they went into a 2-0 lead at the Stadium of Light. They had beaten Bolton Wanderers in the previous round and looked good value for another giant-killing against a Sunderland team who weren't at the races .
Sunderland were deservedly behind after 20 minutes. A long ball out of defence was met by the head of Leon Constantine who flicked on for Colin Larkin, who raced on to the ball and blasted it past Fulop.
The home manager rang the changes after the break as he replaced Healy and Carlos Edwards with Michael Chopra and Kieran Richardson at the start of the second half.
Northampton looked to have put the game beyond doubt when the goalscorer Larkin turned provider, crossing in for Luke Guttridge to fire in Town's second on 80 minutes.
To add insult to injury for the Wearsiders, Nyron Nosworthy limped out of the action to reduce his side to 10 men with all three substitutes having already been used.
But then came the late-late show, with the substitute Anthony Stokes poking home on 85 minutes to give the hosts one last throw of the dice and in time added on the Irishman sealed his double by heading in off the bar to send the game into extra time.
There was no separating the two sides in the extra 30 minutes so it was down to penalty kicks to settle the final result.
Iit was Fulop's chance to shine as thee Sunderland keeper saved Constantine's effort to give the Wearsiders a 4-3 win.
Crewe Alexandra bowed out of the competition at the hands of Liverpool following a 2-1 reverse at Anfield.
The home defender Daniel Agger opened the scoring after 15 minutes with a driven free-kick from 25 yards out.
Michael O'Connor levelled for Crewe 10 minutes later, but the Brazilian midfielder Lucas looped in a header from a Jermaine Pennant cross to seal the win.
The only other League One sides in action on Tuesday night were up against each other, with Leeds United recording a 3-2 victory over Hartlepool United at Elland Road.
Andy Robinson conjured up an injury-time winner after Hartlepool had led twice. With extra-time looming, Jonny Howson played the ball out to Robinson whose shot from the right flew over keeper Arran Lee-Barrett to send Leeds into the fourth round for the first time since 2001.
The Yorkshire side had scored nine goals in their previous two Carling Cup ties this season but they fell behind in the second minute.
Joel Porter helped Ritchie Humphreys' free-kick towards the far post, where Leeds-born Andy Monkhouse climbed unopposed to head into the net.
The lead lasted just 12 minutes as the Hartlepool defender Michael Nelson lost possession to Robert Snodgrass, who sprinted into the penalty box and tucked his shot just inside the left post.
The visitors regained the lead in the 33rd minute when Porter spotted Casper Ankergren off his line and scored from 25 yards.
Ankergren pulled off a desperate save from Ritchie Jones just before the break to prevent Leeds falling further behind, but they levelled again on 57 minutes when David Prutton's cross was lifted on to the bar by Jermaine Beckford and Enoch Showunmi forced home the rebound.
There are six more third round ties on Wednesday. Brighton and Hove Albion are the only League One side in action, they host the Premier League side Manchester City in a delayed second round tie at the Withdean Stadium.