It was all Chelsea in the opening stages, with Southampton barely receiving possession.
However, the hosts were still unable to create any chance or pose a serious threat on goal.
After winning a free-kick from the edge of the area, Marcos Alonso saw his effort deflected off target.
Chelsea went down in their last home clash with Leicester City and a similar outcome would have been the first time this occurred successively on their own patch since 2011.
After back-to-back defeats, Southampton made eight changes with Ralph Hasenhuttl giving a first start in goal to Angus Gunn for Alex McCarthy who were handed a rest.
It's maiden impact came after 15 minutes when a header from Danny Ings was sent over the crossbar from 12-yards.
There was finally a clear sight on goal after Eden Hazard ran onto a loose ball before controlling brilliantly to aim for the top corner, but Gunn read the signs and made the save on 34 minutes.
Four minutes thereafter, the Blues were forced to make a first half change as Ruben Loftus-Cheek came on for a niggling Willian.
Southampton opted to make a change at the start of the second half, with Ings making way for Shane Long.
Stuart Armstrong cautioned the first effort for the Saints which had Kepa Arrizabalaga back-tracking to tip for a corner two minutes from the break.
In an extremely tactical contest, the Blues responded as Jorginho found himself in a good position to get a shot away but it failed to find the target as it sailed over the top after 66 minutes.
Soon, the Londoners thought they had gone in front after Alvaro Moratta finished off a Cesc Fabregas pass only for the far side official to wave his flag for offside.
The Spaniard missed an inviting opportunity to finally get on the scoreboard when he found space on the left side of the penalty area, but his final delivery was poor and straight at Gunn in seeing out the clash.