Jose Mourinho's side arrived at St Mary's on a run of five successive wins in all competitions, although the Barclays Premier League leaders were knocked off their stride early on as Sadio Mane put the hosts ahead.
Hazard ensured they would not be celebrating a memorable win, though, leading an impressive Chelsea recovery by following-up a wonderful leveller with an inspired second-half display, only for resilient Saints to secure a 1-1 draw.
Southampton manager Ronald Koeman will have been a relieved figure at the final whistle, especially after being reduced to 10 men when Morgan Schneiderlin picked up a red card late in a match they started so impressively.
Saints were rewarded for their energetic early display when Mane raced through to meet a wonderful Dusan Tadic pass, keeping calm under pressure from John Terry to beat Thibaut Courtois.
However, Mourinho was not to be undone by former Barcelona colleague Koeman, with Hazard impressively levelling in first-half stoppage time after turning inside and firing home a fine, low strike.
The ever-impressive Belgian continued to threaten in a one-sided second half, yet Saints rode their luck to secure a point.
Hazard enjoyed himself against a Saints defence including teenager Matt Targett - who was making his first Premier League start - and Maya Yoshida as a makeshift right-back.
Chelsea appeared to pinpoint the Japan international in the early stages, with Hazard, Cesc Fabregas and Andre Schurrle all finding space - albeit without seriously threatening Fraser Forster.
A wayward Tadic effort was the best the hosts could muster until they came a Terry clearance away from taking a 14th-minute lead, with Jose Fonte ready to turn home at the far post.
It was a wonderful block but one which only kept Saints at bay for three minutes as an exceptional Tadic ball undid the Chelsea captain.
Mane burst free to latch onto the ball and kept his composure with Terry breathing down his neck, coolly lifting the ball past Courtois.
It was a fine goal - the Senegal winger's second in three days - and one Schneiderlin attempted to add to immediately, only for his long-range effort to fly over.
Seconds later the defensive midfielder was having to work at the other end, cutting out a squared Diego Costa pass as Chelsea attempted to make a quick riposte.
Schurrle was agonisingly close to reaching a chipped Fabregas ball as the visitors upped the ante, although they were still struggling to find the target.
Targett had an effort blocked and Graziano Pelle hooked over as Chelsea continued to be frustrated until first-half stoppage time, when calls for a foul were ignored and Fabregas impressively played through Hazard.
The winger brutally exposed Yoshida, all too easily turning past the defender and, having jinked past Toby Alderweireld, coolly slotted into the far corner.
It was Chelsea's first shot on target and a timely shot in the arm, with Willian brought on for Schurrle at the break.
It did not take him long to make an impact, forcing impressive blocks off Tadic and Alderweireld in quick succession, before Fabregas was booked for alleged simulation.
Referee Anthony Taylor deemed the Spain international to have taken a dive under pressure from Targett, but there appeared contact from the 19-year-old full-back.
Chelsea were now completely on top and Hazard controlled brilliantly then unleashed a strike across the face of goal, before Costa had a close-range effort blocked.
Southampton were penned in their own half, moving Alderweireld to right-back in a bid to stem the flow.
Chelsea smelt blood, though, and Didier Drogba replaced John Obi Mikel as Mourinho looked to strike a knockout blow.
A slip from Costa saved James Ward-Prowse's blushes after under-hitting a back pass, while Filipe Luis threatened late on and Forster was grateful to clear up after Fonte's clearance rebounded goalwards off Victor Wanyama.
Schneiderlin was sent off for a second yellow card with two minutes remaining but Saints held firm to secure a point.
Source : PA