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Southampton were pushing at the other end but were being too easily caught out down the flanks when the ball came back their way.
It was a vulnerability exposed by Norwich in the 68th minute, when Redmond cut inside and lashed home low from the edge of the box, out of Boruc's reach.
The goal led Pochettino to ring the changes, with substitute Jay Rodriguez causing the City backline problems before fellow replacement Steven Davis lashed over.
There was to be no comeback, though, as Norwich stuck to their task to secure victory - with Redmond again going close and Webb waving away another penalty appeal as Snodgrass went down under pressure from Jose Fonte in stoppage time.
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.
In a frenetic, end-to-end clash at a sold-out Carrow Road, the hosts' 19-year-old winger proved the difference as he capped a fine performance with the winner.
Redmond's pace often had Southampton on the back foot and saw him score the decisive goal in the second half, cutting in from the left to unleash a fierce drive from the edge of the box.
The match could have ended quite differently had it not been for the earlier contentious call from referee Howard Webb.
Bradley Johnson clearly handled an Adam Lallana strike in front of Webb, but the referee waved away those claims.