Elias Kachunga, Rajiv van La Parra and Steve Mounie were all guilty of wasting chances as the Terriers, who moved top for a few hours at least as Manchester United face Leicester City in the late game, failed to convert its dominance into a third straight Premier League victory.
Watford and Brighton could not be seperated as they played out a goalless draw at Vicarage Road on Saturday.
Hosts Huddersfield, trailing only Manchester United after two matches on their top-flight return, was kept at bay by Saints goalkeeper Fraser Forster and Mauricio Pellegrino's side improved after the interval, gaining a foothold in midfield and frustrating their newly-promoted opposition.
Huddersfield next face a winless West Ham in London after the global break.
It means that the Saints have scored just once from open play in three games this season, highlighting the side's issues up-front.
Earlier, a scrambled last-gasp victor from Raheem Sterling gave Manchester City a 2-1 victory at Bournemouth.
But seven minutes into stoppage time Sterling linked up with Danilo in the area and his weakly-hit shot took a deflection on its way past a helpless Asmir Begovic.
It's now three clean sheets for Huddersfield, as new signings Jonas Lossl and Matthias Jorgensen have strengthened their back line - but manager Wagner is still seeking new signings before Thursday's transfer deadline.
"It is absolute madness". We were really close to winning but this is football. "Today we deserved to win but they made it incredibly hard for us".