Against a team who had not kept a cleansheet in 10 games in the Premier League, Chelsea failed to score. Against a team who had conceded 21 goals away in the Premier League this season, fewer only than Fulham, Chelsea failed to inspire.
Maurizio Sarri's men had chances but they played too slowly and in long spells of possession, which were frequent, they were ineffective.
The Italian boss will be left frustrated by missed chances from Morata. Stamford Bridge is all too familiar with that feeling.
Ralph Hasenhuttl exclaimed "what is this?" (in English) at one point in a poor first half for Southampton but they leave West London with a massive point that saves them from the ignominy of three consecutive defeats.
Chelsea are now only six points ahead of Manchester United in sixth. Southampton stay in the relegation zone, but with a vital point at a ground where few of their rivals will take anything away this season. The discipline with which Hasenhuttl saw his side defend compactly bodes well for the Saints.
Story of the game
In some games, reporters in the press box rarely get to study the finer details of a manager's face until he is subject to questioning after the final whistle has blown. But, such was the consistent frustration of Maurizio Sarri and Ralph Hasenhuttl at Stamford Bridge that, both managers' faces were on show frequently as they turned and vented at their fellow coaches.
Chelsea spent the opening half an hour with more than 70% of possession, but with it they did little. Their most exciting moments were when they played with greater pace on the counter-attack. The technical ability on display is brilliant when the ball moves from Kepa to Rudiger, into midfield with a deep Jorginho and further forward through Kante before reaching the bright yellow and magical boots of Eden Hazard. But it's all too rare in games against opposition like Southampton. It's why Sarri's side can beat Manchester City but be beaten by Leicester.
The Blues can be a patient side at home, but sometimes it wears thin. And it was only 10 minutes before David Luiz found himself trying to clip a ball over the top of 6ft 5in Jannik Verstergaard for N'golo Kanté to try and win.
They did have chances, as Alvaro Morata headed into the diving hands of Angus Gunn, making his first Premier League start for Southampton at the age of just 22 years and 346 days. It was the Englishman's face which denied Eden Hazard in one of Chelsea's nicest moves of the opening hour.
The Belgian's drifting into the central areas was supported by Morata's awareness as the 26-year-old drifted wide whenever necessary. Hazard found space after the half-hour mark. Rudiger, a constant provider of searching balls, found Hazard and the touch to bring the ball down was fantastic, but the shot struck straight off Gunn's face.
It was Chelsea's best chance of the half, although Morata also saw a curling effort blocked. That shot resulted from quick Chelsea passing on the edge of the box, something that is all too rare. Kante set himself up for a shot before a nice toe to pass it on to Barkley who stretched to feed it further wide on the left side to Morata.
Between those chances, Ruben Loftus-Cheek replaced an injured Willian. With Pedro still out and Callum Hudson-Odio also injured, Sarri is facing difficulties in upcoming matches. His team have so many games this month, with the normal league schedule as well as an FA Third Round tie and a two-legged Carabao Cup semi-final.
Loftus-Cheek is adored at Stamford Bridge more than most of his teammates. An academy player, perhaps the club he represents should take greater note of the benefit of bleeding through the finest talent from their esteemed academy.
Hasenhuttl didn't leave the edge of the pitch throughout the first half and his two exclamations of "what is this?" and "scheisse" were indicative of his side's inability to keep possession in the rare moments that they had it.
The Saints improved slightly after the break as Shane Long replaced Danny Ings. Armstrong won an early corner in the second period with a good long-range effort but that was one of few events in the final third for Hasenhuttl's boys.
Sometimes Hazard doesn't move for a minute or two. He just waits. And then he springs to life, and the roar of Stamford Bridge from all four sides tells you all you need to know.
It was he who came close to bringing the second half to life, firstly as he cut inside past two players and earned a corner with a nice shot and then with a fiercely driven cross through the six-yard box. He was also involved as the linesman's flag prevented a goal on the 70th-minute mark. Morata poked the ball home after a nice move of one-touch football on the edge of the box between Hazard, Fabregas and the Spaniard.
The criticism of Morata will continue, though, because while he finished an easy but offside chance, he couldn't win Chelsea the game. And he should have done, leaning down towards the ground and backwards as his left-foot struck a ball into the body of Angus Gunn from close range. It wasn't in the middle of the box and so that added an element of difficulty, but had he shown greater balance he would have scored. The groans of the Chelsea fans that followed were those of a stadium who knows their striker is very unlikely to be a title-winning one.
Further frustration arrived as N'golo Kante failed to get the ball far enough away from Maya Yoshida to allow him a shot and a winner. Yoshida's tackle in the box was well-timed and vital with Kante set to be through on goal.
That frustrated was replaced by anger very late on as Marcos Alonso was felled in the area by Shane Long as he prepared to shoot and referee Jon Moss waved away any appeals for a penalty.
Although Sarri's team drew more fury when they dithered in defence in added time, it was gasps in the last minute when Rudiger headed back towards his own goal when he was 10 yards away from Angus Gunn in the Southampton box. It was peculiar, but Gunn stayed alert and his left foot steered a long range effort away from goal to cap off a fantastic first start for the Saints.
Takeaways from the game
Chelsea too slow in Sarri-ball
It's not a phrase that their manager himself coined, but it's one that's been used a lot, or at least was at the start of the season when Chelsea were in better form.
Their best moments on Wednesday came on the counter-attack or when someone upped the pace around the box, often Kante. Whatever the long-term plan in terms of style of play, and it seems there is one, things needs to be quicker in the short-term. They can beat City on the counter, but not Leicester or Southampton in possession.
Angus Gunn is a 'keeper
The former-Man City man made his first Premier League start at the age of 22. It was a bold move from Ralph Hasenhuttl with Alex McCarthy being dropped. It was a good one, though.
Gunn denied Hazard with his face and showed he's proactive in his box, coming to clear from Hazard's feet early in the game. He also later stopped Morata in Chelsea's best chance of the second half. It was a good showing.
Yan Vallery impresses against Hazard
This was the Frenchman's seventh appearance in the Premier League. He's had a difficult introduction with a managerial sacking and games against Manchester United, Arsenal, Manchester City and Chelsea.
But he's showing his quality against Eden Hazard at Stamford Bridge. Hazard sought space in the central areas frequently because of Valery's good performance.