Southampton captain Lallana also saw a volley smash against the post and record signing Dani Osvaldo had a close-range effort saved by John Ruddy - missed opportunities the visitors were made to pay for.
Despite Robert Snodgrass being refused a stoppage-time penalty, Redmond's solo effort proved enough to secure Norwich a first league win of the season, ending the visitors' unbeaten start to the campaign.
Ward-Prowse's floated free-kick was only cleared as far as Lallana and the Southampton captain's venomous left-footed volley struck the post.
Mauricio Pochettino's side returned for the second half strongly and Ruddy had to be at his best to deny Osvaldo.
More top news
Heavy showers turning potentially thundery this afternoon. Becoming dry but chilly tonight, then dry and sunny tomorrow.
A wet afternoon with heavy rain followed by heavy, potentially thundery, showers. Dry but chilly tonight, then dry and sunny tomorrow.
Ex-football manager Harry Redknapp told undercover reporters his own players bet on the result of one of their own matches, it is claimed.