
Tonda Eckert's side found themselves in dreamland as goals from Kuryu Matsuki and James Bree gave them a commanding lead within 11 minutes at the promotion favourites.
From that point, Saints faced an onslaught of West Ham pressure, eventually conceding as former Saints right-back Kyle Walker-Peters fired home a stunner.
Thanks to resolute defending and excellent goalkeeping from Daniel Peretz, the away side managed to weather the storm before restoring their two-goal advantage through Lewis Dobbin.
Saints managed to stay ahead throughout the second half, conceding what ended up being a consolation goal from Tomas Soucek in added time.
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"It's probably the thing I'm most pleased about today," Stephens told the Daily Echo when asked about seeing out West Ham's most dangerous spell of the match.
"I think to concede that goal and have a little bit of a wobble for 10 minutes at a ground like this against a team like West Ham...they've got some brilliant players that can really hurt you.
"So to react the way we did and then go up the other end and score again and finish the half so strongly was really pleasing for me.
"We want to win all the time and we were disappointed last week that we didn't get the result we wanted. So to come here and almost lay a marker down for the rest of the season is really big for us."
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The visitors raced out of the traps and fully capitalised on the Hammers' stodgy start as Matsuki rolled in an effort on the rebound before Bree thundered in a screamer on the half-volley.
Saints, as expected, had to suffer in spells but were clinical when they had opportunities of their own.
"We spoke about it during the week. We know that they can be slow starters and they concede a few goals in the first half," the Saints captain revealed.
"So we knew the importance of starting the game really strong and obviously we wanted to get the early goal, but to get two in the first 11 minutes was really good for us.
"It gave us a massive boost in the game and for the majority of the first half I thought we were outstanding and probably could have scored a couple more.
"But we knew, like I said, that we had to start well and we did.
"We knew that it's a massive crowd, it's a big ground, it's a lovely place to play. But we knew that if we could control the game, especially early on, the crowd may turn a little bit," the defender added.
"The expectation on them to win, especially at home, is huge. The size of the club coming down into the Championship, they're expected to win every game. We know that feeling.
"So we knew that if we could get on top early and control that first half with the ball, then we would have a really good chance and that's exactly what we did."
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It was a statement victory for Saints who climbed to sixth in the table onto 20 points. Without their four-point deduction, they would be sitting second, one point off leaders Middlesbrough.
After just 12 games, the season is only a quarter of the way through, but failing to come away with three points would have kept Saints five points off the automatic promotion places.
Jack Stephens goes over to Daniel Peretz after making a stunning save against West Ham (Image: Steven Paston/PA)
On the promotion race, Stephens remained level-headed, saying "At the end of the day, we just need to win games.
"We obviously had the points deduction at the start, which was disappointing, but we didn't want to be playing catch up like we were last year because it can take it out of you a lot when you're constantly trying to catch teams and chase teams down.
"It's really difficult. So we didn't want to give ourselves too much to do.
"We're in a really good position now, very close to the top of the table and that's where we need to be and that's where we want to be, so we'll keep pushing for that."