Nigel Adkins’ side had found life difficult this season, but after defeats to Manchester City and Wigan, the Saints put in an impressive second half display to see off League One side Stevenage and book their place in the third round of the Capital One Cup.
Stevenage, conquerors of Newcastle here at the Lamex Stadium two seasons ago, looked on course to cause an upset early on.
The Hertfordshire side rattled the Southampton bar and dominated against a Saints side that contained 11 changes from the team that crumbled against the Latics last weekend.
Stevenage were made to pay for their profligacy in the second period, however. Tadanari Lee marked his return from a five-month lay-off by putting the Premier League side ahead and they then sealed the match with two goals in two minutes.
Saints’ second came in controversial circumstances. Stevenage captain Mark Roberts miscued a clearance after slipping and the home goalkeeper Chris Day picked the ball up.
Referee Oliver Langford ruled Roberts had intended to pass the ball back to Day, gave a free-kick and a bit of quick thinking from Richard Chaplow allowed Billy Sharp to tap home.
Puncheon stole the show soon after with a peach of a volley and Ben Reeves added a fourth in injury time shortly after Michael Thalassitis had scored a consolation for the home side.
James Ward-Prowse, the latest hot prospect to come out of Southampton’s famed Academy, impressed early on as the away side started brightly.
The 17-year-old midfielder played a wonderful cutting pass to find Sharp, who slotted past Day.
The cheers from the visiting fans were soon silenced, however, as the goal was ruled out for offside.
The move seemed to stun Stevenage as they upped their game and took control of the game in the first half.
Dean Hammond hacked down Luke Freeman on the edge of the box and Greg Tansey curled a wicked free-kick over the wall and on to the frame of the Southampton goal.
Lucas Akins’ hulking figure was causing problems for the Saints back four and Marcus Haber also looked lively, heading just wide after 21 minutes following a scramble in the box.
Ward-Prowse drove just wide shortly after, but Stevenage remained on top.
Robbie Rogers stole the ball off a dithering Chaplow and advanced towards the box before hitting a shot straight at Paulo Gazzaniga in the away goal.
Southampton were struggling to find any rhythm, but Stevenage could not make their dominance pay.
James Dunne released Haber down the middle and he rounded sneaked around the back of Gazzaniga but Daniel Seaborne rescued the Saints.
Another chance came and went just before the break when Roberts found space at the back post but he could only stab in to the side-netting.
Southampton were made to pay for their missed chances eight minutes in to the second half when Sharp surged in to the box and pulled the ball back for Lee, who calmly swept home from 12 yards.
Stevenage were stung by the opener and Southampton started to take control of the game.
Puncheon laid on a clever pass to Sharp at the back post but he curled a speculative shot just over.
Darius Charles thrashed a shot just wide during a rare Stevenage attack and Roberts narrowly missed a header.
Southampton went 2-0 up soon after. Referee Langford gave Saints a free-kick inside the home box after Day picked up a Roberts pass.
Chaplow took the free-kick quickly, laying the ball off to Sharp, who smashed home from 10 yards.
Stevenage’s players were furious with Langford’s decision as a slip from Roberts caused the ball to make its way back to the goalkeeper.
All that was irrelevant as Puncheon wrapped up the win with a contender for goal of the round moments later.
The former QPR man picked up the ball 30 yards out, and lifted it on to his knee before smashing a volley past the stranded Day.
Stevenage restored some pride in injury time when they pulled one back through a 20-yard effort from substitute Thalassitis.