The game was evenly poised at the break but Southampton's early season demons continue to haunt them with yet more poor defending denying them any chance of getting something from this game.
Adkins cut a forlorn figure in the post match press conference, bemoaning his side's defending, and he will know that something will need to change at the back or his side will quickly turn into relegation fodder.
They have now conceded 24 goals this season - a return that is quite simply not good enough.
The corresponding fixture last season saw Saints earn a valuable draw that eventually helped them gain automatic promotion from the Championship at the expense of West Ham.
Southampton have trailed in all eight Premier League games at some point, the only team to be behind in all of their league games.
The Hammers had to rely on the lottery of the play-offs to go up but despite missing out to Saints and Reading on those automatic places, it is Sam Allardyce's experienced West Ham side who have made the better start to the new Premier League campaign.
With 14 points already, the Hammers have a healthy return from their opening eight games while Saturday's game was further evidence that Southampton are yet to settle into Premier League life.
Saints took the decision to drop star striker Rickie Lambert prior to the game but the visiting side made a bright start without creating a clear opening. The first real chance fell West Ham's way with Jos Hooiveld heading James Tomkins' looping header from 12 yards off the line.
James Collins later went close with a header but by and large this was a poor first half played in a turgid atmosphere with the moans and groans of the Upton Park faithful growing louder as the half wore on.
Allardyce also cut a frustrated figure on the sidelines chewing gum with more urgency and intensity than his lack-lustre side, while for Adkins it was a case of job done as the teams went into the half-time break level.
But it took just 58 seconds for the Hammers to buck up their ideas and typically it came from poor Southampton defending with no-one dealing with Noble's inswinging 35-yard free kick that eventually bounced in at the back post.
It was the 21st goal Saints had conceded this season, a symptom of their early-season troubles and just a minute later there was worse to come for Adkins' side.
Yossi Benayoun showed more desire to get to the ball than Maya Yoshida and his cross to the back post was tapped into the empty net by Nolan.
Allardyce delight with victory
With Upton Park lifted and the supporters buoyed, Southampton's confidence evaporated as the away fans called for their talisman to be introduced - Lambert.
But it was the man that was playing up front in his place - Jay Rodriguez - who helped get Saints back in the game, showing quick feet to turn inside Collins before releasing Lallana. With his back to goal the midfielder swivelled delightfully before powering a shot into the roof of the net.
Lambert was then introduced and he went desperately close with a free kick from 20 yards.
But the Hammers soon restored their two-goal advantage with another Noble free kick causing Saints problems and Jose Fonte was penalised for handball after coming under pressure from Andy Carroll.
Noble powered in the spot kick to a collective sigh of relief and Carroll continued to cause Hooiveld problems at the back before he was replaced to a standing ovation.
The on-loan Liverpool striker is quickly on his way to becoming a cult hero at Upton Park.
West Ham pressed for a fourth and it came late on through Maiga who sealed the rout with a wonderful solo goal that embarrassed three Southampton defenders.
Guly Do Prado fouled by Jordan Spence, the ref awards a free kick. Guly Do Prado takes the direct free kick.
The ball is swung over by Gary O'Neil, Headed effort on goal by Kevin Nolan from inside the penalty box misses to the right of the goal.
Short corner worked by Gary O'Neil.
Guly Do Prado handles the ball and concedes a free kick. Indirect free kick taken by Mark Noble. Modibo Maiga is flagged offside by the assistant referee. Artur Boruc restarts play with the free kick.
Modibo Maiga concedes a free kick for a foul on Nathaniel Clyne. Free kick taken by Morgan Schneiderlin.
Substitution James Ward-Prowse is brought on as a substitute for Steven Davis.
Centre by Steven Davis, Header from deep inside the area by Maya Yoshida goes over the bar.
Substitution Jordan Spence comes on in place of James Tomkins.
Assist by Kevin Nolan.
86:08 Goal scored
Goal - Modibo Maiga - West Ham 4 - 1 Southamp'n Modibo Maiga scores a goal from deep inside the penalty area to the top left corner of the goal. West Ham 4-1 Southampton.
Emmanuel Mayuka takes a shot. Jussi Jaaskelainen makes a save.
Maya Yoshida crosses the ball, James Collins makes a clearance.
Mark Noble takes a inswinging corner from the left by-line to the near post, Morgan Schneiderlin makes a clearance.
Free kick awarded for an unfair challenge on James Collins by Rickie Lambert. Jussi Jaaskelainen takes the free kick.
Substitution Modibo Maiga is brought on as a substitute for Andy Carroll.
Mark Noble restarts play with the free kick.
Booking Morgan Schneiderlin booked.
Unfair challenge on Andy Carroll by Morgan Schneiderlin results in a free kick.
Maya Yoshida sends in a cross, The referee blows for offside against Rickie Lambert. Free kick taken by Jussi Jaaskelainen.
Gary O'Neil takes the direct free kick. Mark Noble takes a shot. Blocked by Rickie Lambert.
Booking Jos Hooiveld is booked.
Foul by Jos Hooiveld on Andy Carroll, free kick awarded.
Free kick awarded for a foul by Yossi Benayoun on Jose Fonte. Direct free kick taken by Jose Fonte.
Inswinging corner taken from the left by-line by Mark Noble, clearance made by Jos Hooiveld. Free kick awarded for a foul by James Collins on Jos Hooiveld. Direct free kick taken by Artur Boruc.
Emmanuel Mayuka challenges Kevin Nolan unfairly and gives away a free kick. George McCartney restarts play with the free kick.
71:20 Goal scored
Goal - Mark Noble - West Ham 3 - 1 Southamp'n Mark Noble scores a power penalty. West Ham 3-1 Southampton.
Jose Fonte is penalised for handball and concedes a .
Free kick awarded for an unfair challenge on Andy Carroll by Jos Hooiveld. Free kick taken by Mark Noble.
Centre by Nathaniel Clyne, Close range headed effort by Rickie Lambert goes wide of the left-hand post.
Substitution Mohamed Diame leaves the field to be replaced by Gary O'Neil.
Unfair challenge on Adam Lallana by Winston Reid results in a free kick. Strike comes in from Rickie Lambert from the free kick.
Andy Carroll takes a shot. Jose Fonte gets a block in.
Substitution Jason Puncheon goes off and Emmanuel Mayuka comes on.
Substitution (Southampton) makes a substitution, with Rickie Lambert coming on for Jay Rodriguez.
Jay Rodriguez provided the assist for the goal.
62:56 Goal scored
Goal - Adam Lallana - West Ham 2 - 1 Southamp'n Adam Lallana finds the back of the net with a goal from inside the box high into the middle of the goal. West Ham 2-1 Southampton.
The assistant referee flags for offside against Kevin Nolan. Free kick taken by Morgan Schneiderlin.
Kevin Nolan takes a shot. Save by Artur Boruc.
Andy Carroll fouled by Morgan Schneiderlin, the ref awards a free kick. Direct free kick taken by Mark Noble.
Maya Yoshida takes a shot. James Collins gets a block in.
The offside flag is raised against Jay Rodriguez. Indirect free kick taken by Jussi Jaaskelainen.
Guly Do Prado crosses the ball.
Guly Do Prado concedes a free kick for a foul on Mark Noble. Free kick taken by Jussi Jaaskelainen.
Yossi Benayoun provided the assist for the goal.
47:30 Goal scored
Goal - Kevin Nolan - West Ham 2 - 0 Southamp'n Kevin Nolan finds the net with a goal from inside the six-yard box to the bottom left corner of the goal. West Ham 2-0 Southampton.
Assist by Andy Carroll.
45:56 Goal scored
Goal - Mark Noble - West Ham 1 - 0 Southamp'n Free kick scored by Mark Noble. West Ham 1-0 Southampton.
Foul by Jos Hooiveld on Andy Carroll, free kick awarded.
Jos Hooiveld gives away a free kick for an unfair challenge on Andy Carroll. Mark Noble takes the free kick.
The second half has started.
45:00 +1:22 Half time
Half Time The match has reached half-time.
The ball is swung over by Matthew Jarvis, Jose Fonte gets a block in.
Adam Lallana is caught offside. Indirect free kick taken by Jussi Jaaskelainen.
George McCartney concedes a free kick for a foul on Jason Puncheon. Morgan Schneiderlin restarts play with the free kick.
Outswinging corner taken by Mark Noble from the right by-line.
Inswinging corner taken by Mark Noble, clearance by Jos Hooiveld.
Adam Lallana concedes a free kick for a foul on James Tomkins. James Collins takes the free kick. Foul by Nathaniel Clyne on Matthew Jarvis, free kick awarded. The free kick is delivered right-footed by Mark Noble from left wing,
Guly Do Prado takes a shot and missed to the left of the target.
The assistant referee signals for offside against Jason Puncheon. Indirect free kick taken by Jussi Jaaskelainen.
Shot from outside the box by Maya Yoshida goes wide right of the target.
Jos Hooiveld concedes a free kick for a foul on Mohamed Diame. Mark Noble takes the direct free kick.
Foul by Winston Reid on Jason Puncheon, free kick awarded. Jay Rodriguez restarts play with the free kick.
Centre by Nathaniel Clyne.
The assistant referee signals for offside against Yossi Benayoun. Maya Yoshida restarts play with the free kick.
Free kick awarded for a foul by James Collins on Adam Lallana. Strike on goal comes in from Jay Rodriguez from the free kick.
George McCartney challenges Morgan Schneiderlin unfairly and gives away a free kick. Direct free kick taken by Artur Boruc.
Andy Carroll produces a cross, clearance by Steven Davis.
The referee blows for offside against Jay Rodriguez. James Collins takes the indirect free kick.
Jay Rodriguez produces a right-footed shot from the edge of the box and misses to the right of the goal.
Mark Noble takes the inswinging corner, save by Artur Boruc.
The ball is swung over by Matthew Jarvis, James Tomkins takes a shot. Clearance made by Jos Hooiveld. Save made by Artur Boruc.
Free kick awarded for a foul by Morgan Schneiderlin on Kevin Nolan. Mark Noble takes the direct free kick.
Inswinging corner taken by Jason Puncheon from the right by-line, Jos Hooiveld takes a shot. Save by Jussi Jaaskelainen.
The ball is swung over by Nathaniel Clyne, George McCartney gets a block in.
Jay Rodriguez crosses the ball, James Collins gets a block in.
The offside flag is raised against Jay Rodriguez. Jussi Jaaskelainen takes the free kick.
A cross is delivered by Yossi Benayoun, Jose Fonte manages to make a clearance.
The ball is delivered by Jason Puncheon, George McCartney makes a clearance. Maya Yoshida delivers the ball, George McCartney makes a clearance. Jason Puncheon takes the inswinging corner, Andy Carroll makes a clearance.
Nathaniel Clyne sends in a cross, clearance made by Winston Reid.
Andy Carroll takes a shot. Blocked by Jose Fonte.
Inswinging corner taken from the right by-line by Jason Puncheon, James Tomkins manages to make a clearance.
Adam Lallana fouled by Winston Reid, the ref awards a free kick. Adam Lallana takes the direct free kick.
The ball is delivered by Matthew Jarvis, clearance by Maya Yoshida.
The game gets underway.
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