Visitors Chelsea went into the afternoon holding a perfect record having won all seven of their matches conceding just three times in the process.
That all changed on the south coast as Southampton delivered an excellent collective showing to cruise to victory.
“We dominated from start to finish,” Fleming said. “Defensively we were very solid, we kept our shape and pressed well when it was on. At the other end, we made lots of chances. What can I say, we were just excellent today.
“There have been times this season where we have defended strongly but lacked a cutting edge in the final third or threatened in attack but been loose at the back. That wasn’t the case here, we put in a complete performance all over the field.
“Chelsea are a very good side, they are top of the league and had been scoring for fun before today. This result shows what this group is capable of. They put everything together and delivered, I am absolutely delighted.”
Southampton will take on West Brom at the St Mary’s Stadium in the Premier League today.
West Brom are just one point ahead of Southampton in the table, but have not won once in their past five leagues games.
Southampton last time out played a thrilling 2-2 draw with Newcastle, with Manolo Gabbiadini scoring twice on his return.
The two-goal hero is expected to start for the Saints against West Brom.
Speaking ahead of the game, Southampton manager Mauricio Pellegrino said: "It is a fact we are not getting really good results [at home], and not just from this season.
"Some players who have more time here than me can feel this anxiety, but it is something which is normal.
“At the top level, things can be up and down, but this is in every single game, and you have to survive, to challenge these kinds of moments.”
So, if you want to live stream all the action - here’s Express.co.uk’s guide to watching the game online.
Sofiane Boufal came off the bench to run 70 yards through West Brom’s tiring midfield and defence to score a wonderful solo goal and light up a drab evening on the South Coast.
The Saints were ready to reflect on more of their goal-scoring woes as they missed a string of chances and found Albion’s Ben Foster in inspired form, having spent almost the entire 90 minutes in the Baggies’ half.
Even before Storm Brian began whipping its way along the South coast, expectations of a goal-laden display of Premier League brilliance seemed unlikely.
There had been only 21 of them scored in the previous 14 meetings between the two sides and the conditions weren’t helping.
Tony Pulis’ side did what they do best: sit deep, clog up the midfield and wait for their chance to come on the break.
Whilst the Baggies picked up a commendable point at Leicester on Monday night, they were without a win since August after two wins in the opening three games.
The perfect time then to visit a Southampton side that has failed to score nine times at home in 2017, though Manolo Gabbiadini did so twice in the draw with Newcastle last week.
The only first-half chances there went to Southampton, with the game being played almost exclusively in the Baggies’ half.
72’ - Dusan Tadic with Southampton’s best chance of the match!
He finds himself with the ball at his feet with bags of time inside the West Brom penalty area but Ben Foster is speedily off his line to deny the winger.
Just seconds later Fraser Forster is forced into action at the other end as he tips Nacer Chadi’s curled effort from distance over the crossbar.