However, the hosts were level three minutes later as Teemu Pukki headed in Max Aarons' cross at the near post.
The equaliser was Norwich's sole attempt in an otherwise entirely one-sided first half. A dominant Saints registered 12 shots on goal but Adams was denied by Tim Krul at close range with the visitors' best chance shortly before half-time.
Smith's men were much improved following the interval, Milot Rashica forcing Alex McCarthy into action while the Saints goalkeeper sprang to his near post to deny Pukki a fine solo goal with 15 minutes remaining.
He was unable to reach Hanley's header, though, as Norwich survived late Southampton pressure to secure a winning start to Smith's reign.
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