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
Simon's Blog - Things That Look Like Other Things
Tuesday Evening's Pollen Forecast
Tuesday night's forecast for the west of the region