Southampton have scratched their seven-year itch. That is how long it has taken the south coast club, once home to Channon, Keegan, Shearer and Le Tissier, to return to the Premier League. There has been a drop into administration and League One football along the way, but with this emphatic, deserved victory the Saints have completed their march out of the darkness.

The outpouring of joy at the final whistle was understandably uncontrollable. Despite pleas from the public-address announcer for supporters to refrain from charging on to the pitch, the bulk of the 32,363 crowd – a record for this venue – could not help themselves. They flooded on to the turf while some released red flares into the gloomy and damp south-coast sky. In the midst of it all Rickie Lambert, Southampton's top scorer and recently named PFA Championship player of the year, could be seen looking on with a mixture of bewilderment and pleasure. His face captured perfectly the story of this club's achievement.

For it was hard to see a way back for Southampton when, three years ago this month, and after an era of chaotic mismanagement, the club was plunged into administration and hit with a subsequent 10-point penalty. Relegation to League One soon followed and, at that point, a return to the top-flight, where they last played in 2005 under the management of Harry Redknapp, seemed a lifetime away.

But the turnaround has been swift. Swiss businessman Markus Liebherr – who died in 2010 – led a takeover that brought the club out of administration. Since then, under the chairmanship of the outspoken Italian banker Nicola Cortese and, just as crucially, the management of Nigel Adkins, Southampton have achieved back-to-back promotions.

It has been no fluke. Under Adkins, the former Scunthorpe manager, Southampton have never been out of the Championship's top-two places, are the division's highest scorers with 85 goals and have finished with a home record, having won 16 of their 23 games.

Tension has taken over in recent weeks, however, and Southampton had won two of their previous six games, a spell that included defeat to the champions, Reading. That meant Southampton, so long red-hot favourites for promotion, came into this contest still fearing the worst: fail to beat Coventry and they could yet be pipped to second place by West Ham.

It came as little surprise, then, to see the hosts start in tentative fashion. Unable to keep possession in their traditional manner, Southampton found themselves pushed further and further back by a Coventry side that seemed to free of all inhibitions having been relegated to the third tier for the first time since 1964 following a wretched campaign in which they finished 23rd and as the division's lowest scorers.

It was Andy Thorn's side who came closest to opening the scoring when their captain, Gary McSheffrey, hit an accurate, curling drive towards the corner that forced Kelvin Davies into a fine, diving save.

Southampton found their composure, however, and took the lead on 16 minutes in typically eye-catching style. Having practically carried the ball from one area to another, José Fonte played a pass out wide to Guly do Prado, whose quick sideways delivery was struck by Adam Lallana and diverted into the net by Billy Sharp. Three minutes later Fonte scored, heading Daniel Fox's right-wing corner past the grasp of the Coventry goalkeeper, Joe Murphy.

From there, and with the home crowd's roars reaching fever pitch, the outcome was never in doubt. Jos Hooiveld got Southampton's third from close range after 59 minutes before Lallana sealed the rout with his 13th goal of the season four minutes later.

Trips to Old Trafford, the Etihad Stadium, Anfield and Stamford Bridge await Southampton, then, not to mention an estimated £90m boost to the club's coffers. Having lost Gareth Bale, Theo Walcott and, most recently, Alex Oxlaide-Chamberlain to Premier League clubs since their relegation under Redknapp, Southampton can now focus on attracting high-calibre talent themselves, with Adkins stating that their preparations for next season have already begun.

The manager also insisted that his side would, like Norwich and Swansea, continue to play with a high-tempo, possession-based style among the elite, an approach that ultimately left Coventry in a ragged state here. Like Southampton, they, too, were once regular Premier League performers. Heading towards oblivion, they should take inspiration from how their opponents have risen from despair to glory.