Had the mercurial Italian Gianfranco Zola tapped in an unchallenged, simple six-yarder after 12 minutes, the story may have been different.
However the ball from Jimmy Floyd Hasselbaink must have been too perfect and Zola somehow managed to hit Southampton's left upright and the ball screwed along the goal-line before being cleared.
Chelsea boss Claudio Ranieri blamed the Stamford Bridge pitch for his side's poor showing: "I'm worried about the pitch and we will have it changed after the match against Charlton Athletic on January 11.
"It was not a good pitch for us. We love to play the beautiful game but it was not possible today.
"Southampton play an easy, efficient game and on that pitch adapted better. But last season, we lost 4-2 to Southampton so I suppose I must be happy with the point."Southampton manager Gordon Strachan agreed that the pitch was bad, but his team adapted well to it, joking: "That pitch is very like our training ground one and we are not even allowed to play on it.
Strachan summed up his team as hard working, adding: "We are confident that we can stand toe-to-toe with anyone, but we also know that if we don't do the right things we can also get beaten.
"But we are doing well. We could have won it but I'm happy that we attacked well and defended well."Saints could have won the game as they had more efforts on target than the second placed side. But Chelsea had the clearer goal scoring efforts.
Had Hasselbaink shown more composure nine minutes from time when he was put clean through by Zola, Chelsea could have sneaked it, but the Dutchman took one touch too many before getting his left footed shot off which flashed across the goal line.
Substitute William Gallas had a fine effort saved by the excellent Antti Niemi a minute from time and Desailly somehow arrowed the ball high over the bar from six yards out.