Diego Costa's fifth goal in his last six league games gave Chelsea - seeking to capitalise on Manchester City's surprise 1-0 defeat to Burnley - an early lead, although that lasted just eight minutes thanks to Dusan Tadic's penalty.
Ronald Koeman's side threatened to add a second against a home side appearing somewhat fatigued following Wednesday's UEFA Champions League exit to Paris Saint-Germain.
However, while Jose Mourinho's men were far from their fluent best, they always looked the more likely to grab a winner after the break, with Costa striking a post before Fraser Forster denied Willian, Eden Hazard and substitute Loic Remy.
Chelsea were ultimately unable to break through, but now lead nearest rivals City by six points at the top of the table and still hold a game in hand.
Southampton are likely to be heartened by a point as they maintain their bid for a European place, while Mourinho will hope his side can rediscover their killer touch as they bid to make his prediction of Premier League glory a reality.
Willian was one of two Chelsea changes and the Brazilian posed early problems for Southampton down the right, but it was frontman Costa who opened the scoring 11 minutes in.
Branislav Ivanovic delivered a deep cross from the right following Hazard's lay-off, and an unmarked Costa had the simplest of tasks to head home and register his 19th goal of the season.
Southampton would have been level soon after were it not for a smart save from Thibaut Courtois that denied Sadio Mane.
However, after Mane had been brought down in the box by Nemanja Matic, who received a yellow card for his mistimed challenge, Courtois was beaten by Tadic from 12 yards despite getting a foot to the ball.
The equaliser buoyed Koeman's side and the pace of Tadic, Mane and the recalled Shane Long caused John Terry's backline plenty of problems.
Matic was perhaps fortunate not to see a second yellow for another foul on Mane after the break.
The fit-again Toby Alderweireld, making a first start since January due to a recent hamstring problem, saw the resulting free-kick saved by Courtois before Mourinho opted to replace Matic with Ramires.
Costa was back in the thick of it before the hour mark as he saw penalty appeals waved away following a tangle with Jose Fonte before diverting Willian's wayward strike onto Forster's right-hand post.
A jinking run from Tadic failed to bring about a second for Southampton and Forster then proved the hero as he kept out efforts from Willian, Hazard and Oscar in the latter stages.
Remy was the next to be denied by Forster before Terry fired wide in a dramatic finale that saw the Stamford Bridge faithful ultimately left frustrated.
