Forster twice denied Mesut Ozil in the first half as Arsenal struggled to create opportunities.
He was even busier in the second half as the hosts pressed for a breakthrough, making one flying save to keep out a curler from Olivier Giroud and two efforts from Theo Walcott who came on as a substitute.
Arsenal forward Alexis Sanchez, making his first start since November after returning from injury, had another effort cleared off the line as Southampton hung on.
The Gunners have now slipped to fourth spot.
(Reporting by Martyn Herman; editing by Toby Davis)
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