After a promising, even first half nevertheless lacking in goalmouth action aside from three spurned chances for Mesut Ozil, the Gunners turned up the pressure after the break and threatened regularly, only to find Forster in their way.
The England international denied Olivier Giroud on multiple occasions as well as former Saint Theo Walcott, while James Ward-Prowse cleared off the line from Alexis Sanchez, all part of an accomplished defensive display from Ronald Koeman’s men.
With Manchester City and Tottenham winning elsewhere, Arsenal’s failure to break through sees them drop below their north London rivals on goal difference and five points adrift of leaders Leicester City, while Saints climb to seventh.
A sublime piece of skill from Ozil in the 12th minute nearly lit the blue touch-paper after a tight start, the German plucked a Sanchez pass out of the air only to see Forster save with his feet.
Southampton – who were without January signing Charlie Austin through injury – quickly registered their first chance less than a minute later, Sadio Mane unable to beat Petr Cech at his near post from Shane Long’s flick.
Ozil was presented with another opportunity midway through the half after Giroud had met a Hector Bellerin cross, the midfielder diverting the ball towards goal but again being denied by Forster.
The visitors finished the half strongly and saw Mane, Tadic and Oriol Romeu all fail to test Cech from promising positions.
With half-time approaching, a mazy run from Joel Campbell almost lifted the frustration inside the Emirates Stadium but Ozil was again unable to turn the ball home.
Forster was again on hand three minutes after the break to keep the hosts at bay, comfortably pawing away a curling effort from Giroud.
Despite the growing anxiety coming from the home fans, Arsenal continued to create chances but lacked quality in front of goal with Sanchez and Giroud wasteful.
Substitute Walcott was next to have a sight of goal after 67 minutes. However, Forster made an impressive double save to deny the ex-Saints forward.
When Arsenal were finally able to get the ball past the 27-year-old keeper, Ward-Prowse rescued Forster, the midfielder clearing off the line to deny Alexis.
The hosts still needed to be alert at the back as the pace of Mane caused problems but Southampton were equally as profligate in front of goal, Koeman’s side grateful to one final save from Forster to leave Arsenal with one point from the sides’ two league meetings this season.