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.
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The latest weather for the east with Philippa
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Met Office issues storm warnings overnight as 80mph winds are expected across the south and east. Storm Imogen is due at around 3am