Morgan Schneiderlin got the hosts off to a dream start as they took the lead after just five minutes when a smart through ball from Gaston Ramirez found the 24-year-old striding forward and he calmly slotted past John Ruddy.
It took Norwich just over half an hour to have their first effort on goal as Gary Hooper skewed his strike well wide.
Rickie Lambert replaced Adam Lallana on the 57-minute mark and he wasted no time - 65 seconds to be precise - in having an impact. The striker brought the loose ball down from the air, turned away from Joseph Yobo before firing past Ruddy.
Jay Rodriguez then looked as though he had wrapped things up for the hosts from close range after second-half substitute Guly do Prado saw his effort blocked by Ruddy and Lambert teed up his England team-mate for the simple finish.
Late goals from Johan Elmander and Robert Snodgrass following defensive errors threatened a comeback for the visitors, but following Steven Davis' swift break, Sam Gallagher netted his first Premier League goal in stoppage time to seal the win.
Chris Hughton made five alterations to the side held 1-1 draw by Stoke last weekend, so it was perhaps no surprise that they began shakily.
Ramirez, making his first league start since New Year's Day, headed over inside the opening 90 seconds and then provided the opening goal with just five minutes on the clock.
Davis, Rodriguez and Ramirez were all involved in the move, with the latter playing a wonderfully weighted ball through for Schneiderlin to turn past Ruddy.
Davis glanced a header wide soon after the Frenchman's 10th goal for Saints, before Yobo used his strength and experience to stop Rodriguez getting a shot away after latching onto a fine Lallana pass.
James Ward-Prowse did well to stop Hooper capitalising on defensive confusion in a rare moment of respite for Norwich, who soon saw Davis and Ramirez come close from the edge of the box.
Referee Kevin Friend waved away appeals from Norwich's players for handball against Jose Fonte on the edge of the Saints box.
Eight City players surrounded the referee in the next break of play, which was soon followed by Hooper wasting Norwich's best chance of the half by firing into the side-netting.
The Saints were in the ascendancy at the break and things looked set to continue in the second half.
Ward-Prowse forced Ruddy into action with a 25-yard strike, before the teenager sent in a corner which Rodriguez nodded just wide.
In an attempt to put the match to bed, Pochettino surprisingly withdrew captain Lallana after 57 minutes - but it reaped immediate rewards.
Fonte's long ball was flicked on as Ramirez put pressure on the Norwich defence, with the ball falling kindly for Lambert, who turned past Yobo and slotted impressively past Ruddy.
The goal saw Hughton take drastic action, bringing on Elmander, Nathan Redmond and Ricky van Wolfswinkel in the 65th minute.
However, Saints soon pulled further ahead. Ruddy did wonderfully to deny substitute Guly, but the rebound fell for Lambert to flick onto Rodriguez to net.
The England forward rattled the crossbar with an incredible long-range effort and Ruddy denied Lambert as Saints looked to pull further ahead, before Norwich launched an improbable comeback.
With 85 minutes on the clock, a wayward Fonte backpass fell kindly for Elmander and the on-loan striker slotted coolly past Boruc.
Next, Guly was the guilty party, losing possession as Van Wolfswinkel tested Boruc and Snodgrass struck home the rebound.
It was an ending few could have predicted but Saints soon broke to put the game out of sight.
A slip from Yobo saw Davis race through and square for teenager Gallagher, whose shot crossed the line before it was hacked away.