The winger, on loan from West Ham United, fired a free-kick straight into the Northampton wall, but made no mistake when he was handed a second chance minutes later.
The 19-year-old fired over the wall and saw the ball bounce in front of Cobblers keeper Chris Dunn and into the net with 93 minutes on the clock.
Southend had the better chances early on in a fairly even first half. The first came after seven minutes when Northampton goalkeeper Chris Dunn dived at the feet of the onrushing Alex Revell as he bore down on goal.
Seven minutes later Dougie Freedman fired wide of the right post from 14 yards after being teed up by Revell's square ball.
And Peter Clarke headed a Rob Milsom corner from the right wide after meeting the ball at the near post.
Northampton's first chance came in the 32nd minute when Adebayo Akinfenwa set up Kyle Walker, but Blues goalkeeper Steve Mildenhall palmed clear his 25-yard shot.
Walker then lashed a Liam Davis cross from the left well over the bar when he should have done better.
The Shrimpers replied with Simon Francis releasing Osei Sankofa to the right byline, but his cross missed the outstretched Revell and deflected across the face of the goal off Jason Crowe.
The Cobblers had the last say of the half when Akinfenwa toed a shot straight at Mildenhall.
After the break Alan McCormack and Milsom were off target for Southend, while Giles Coke and Leon Constantine did the same at the other end.
Southend created their best chance so far on the hour mark when Mildenhall's kick found Freedman, who passed to Revell who in turn fed Stanislas. The winger beat two men but saw his shot deflect off Dunn for a corner.
Southend fans were screaming for a goal after Dunn caught Revell's looping header from Stanislas' left-wing cross and took a step backwards. But their appeals were in vain.
The Cobblers were reduced to ten men in the 76th minute when Abdul Osman was sent off for a second bookable offence after felling Johnny Herd.
Southend were unable to make their extra man count, until Stanislas fired in the winner three minutes into stoppage time.
Shrimpers boss Steve Tilson was overjoyed: "It was a huge relief to see Junior's goal go in and it was certainly the best Christmas present I could've asked for. The lads could not be faulted for effort because they gave everything but I thought it was going to be another one of those days. We missed some good chances and you start to fear that it isn't going to happen but in the end I felt we deserved to win because we had been knocking at the door for quite some time."
Cobblers boss Stuart Gray was disappointed: "The referee had shown that he was getting his card out for any mistimed tackle and Abdul did two of those so we felt he was unfortunate but possibily in the eyes of the referee he had to walk. It was a game of few chances, but we had the better of them in the first half but didn't take them. Then we invited pressure on ourselves by giving away silly free kicks late in the game and if you give enough of them away then you will be punished. We said at half time that the game was there to be won. I felt they were nervous and had we got the first goal we would have won, but we didn't take advantage of those first half chances.
The 19-year-old fired over the wall and saw the ball bounce in front of Cobblers keeper Chris Dunn and into the net with 93 minutes on the clock.
Southend had the better chances early on in a fairly even first half. The first came after seven minutes when Northampton goalkeeper Chris Dunn dived at the feet of the onrushing Alex Revell as he bore down on goal.
Seven minutes later Dougie Freedman fired wide of the right post from 14 yards after being teed up by Revell's square ball.
And Peter Clarke headed a Rob Milsom corner from the right wide after meeting the ball at the near post.
Northampton's first chance came in the 32nd minute when Adebayo Akinfenwa set up Kyle Walker, but Blues goalkeeper Steve Mildenhall palmed clear his 25-yard shot.
Walker then lashed a Liam Davis cross from the left well over the bar when he should have done better.
The Shrimpers replied with Simon Francis releasing Osei Sankofa to the right byline, but his cross missed the outstretched Revell and deflected across the face of the goal off Jason Crowe.
The Cobblers had the last say of the half when Akinfenwa toed a shot straight at Mildenhall.
After the break Alan McCormack and Milsom were off target for Southend, while Giles Coke and Leon Constantine did the same at the other end.
Southend created their best chance so far on the hour mark when Mildenhall's kick found Freedman, who passed to Revell who in turn fed Stanislas. The winger beat two men but saw his shot deflect off Dunn for a corner.
Southend fans were screaming for a goal after Dunn caught Revell's looping header from Stanislas' left-wing cross and took a step backwards. But their appeals were in vain.
The Cobblers were reduced to ten men in the 76th minute when Abdul Osman was sent off for a second bookable offence after felling Johnny Herd.
Southend were unable to make their extra man count, until Stanislas fired in the winner three minutes into stoppage time.
Shrimpers boss Steve Tilson was overjoyed: "It was a huge relief to see Junior's goal go in and it was certainly the best Christmas present I could've asked for. The lads could not be faulted for effort because they gave everything but I thought it was going to be another one of those days. We missed some good chances and you start to fear that it isn't going to happen but in the end I felt we deserved to win because we had been knocking at the door for quite some time."
Cobblers boss Stuart Gray was disappointed: "The referee had shown that he was getting his card out for any mistimed tackle and Abdul did two of those so we felt he was unfortunate but possibily in the eyes of the referee he had to walk. It was a game of few chances, but we had the better of them in the first half but didn't take them. Then we invited pressure on ourselves by giving away silly free kicks late in the game and if you give enough of them away then you will be punished. We said at half time that the game was there to be won. I felt they were nervous and had we got the first goal we would have won, but we didn't take advantage of those first half chances.
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