The league's newcomers were unbeaten in their opening two games, but they were taught a harsh lesson after conceding four second-half goals in the space of just 19 minutes.
The home side managed to create the better chances early on and Saints captain Lee Clarke had the first shot on goal after three minutes.
He turned neatly in the box, but his effort was straight into the arms of Shots goalkeeper Nikki Bull.
Four minutes later it was the Saints' Adam Wilde who went close, curling a free-kick from the edge of the box just over after Tom Davis had been fouled.
The Shots then began to dominate proceedings and their first chance came from the experienced Darren Barnard after nine minutes. He tried his luck with a free-kick from 30 yards out, but was well off-target.
The home side were struggling to get their passing game together and they fell behind in first-half injury-time. Ryan Williams burst into the box after a neat one-two, and as Pail Bastock came out, the winger went to ground.
It looked like a dive but the referee Declan Ford had no hesitation pointing to the spot and Barnard scored the resulting spot-kick.
Saints boss Colin Lippiatt was furious at the decision to award the penalty, but his side were back on level terms just minutes after the break.
Clarke skipped past his marker and fired in an effort which was deflected across goal and Ram Marwa was on hand to apply a right-foot finish from six yards.
The away fans didn't have to wait too long for the next goal. John Grant was slipped through by Marcus Gayle and the forward raced to the touchline before cutting the ball back for Williams, who applied the finish from close range.
The home side looked at all sea and they fell further behind on 60 minutes when Grant connected superbly with Dean Smith's cross to score with a right-foot volley which went in off the post.
The game was up for Saints minutes later when Grant latched on to a through ball and rounded Bastock to slip it home.
It got worse for the home side a minute later when Gayle headed home a superb cross from Louis Soares.
The home side did manage two late consolation goals. Two minutes from time, Tom Davis had his heels clipped in the box by Williams and got up to convert the penalty, before Dean Cracknell deflected a Rob Norris shot past Bull in the final minute.