According to football411.com website, chances were at a premium for much of the first half. Robert Snodgrass tested Gazzaniga in the third minute, his rising drive stinging the palms of the Argentinian, while Adam Lallana saw his left-foot volley flash just over Mark Bunn's bar.
Rickie Lambert got the breakthrough for Saints just after the half-hour mark. Lallana swung in a free-kick which was flicked on by Gaston Ramirez and the big forward stuck out a boot to prod the ball home.
It could have been two had anyone reached Morgan Schneiderlin's superb cross a few minutes later but it drifted just wide.
Norwich levelled just on half-time thanks to another free-kick. Snodgrass' low effort should have been easy for Gazzaniga but the keeper was slow to get down and allowed the ball to squirm into the net.
Saints started the second half brightly with Lambert winning the ball in the box but directing his header straight at Bunn.
Gazzaniga made amends for his earlier error midway through the half, keeping out a close-range header from Grant Holt, and minutes later Bunn did well to steer a curling effort from Jason Puncheon past the post.
However, neither side was able to find a winner and the game ended in stalemate.
Norwich have now drawn their last four away games while Southampton have taken seven points from their last three matches.