Chelsea striker Alvaro Morata was again on the bench after a back injury, as Antonio Conte continued with his front three of Hazard, Willian and Pedro.
BBC Sport shared the two lineups:
The first half was a tight affair, although the hosts had the better of the opportunities. Willian was the first to go close, swapping passes with Alonso before firing just wide after 14 minutes.
Southampton goalkeeper Fraser Forster then saved a speculative effort from Tiemoue Bakayoko before tipping an Alonso effort around the post.
Sports reporter Matt McGeehan felt the Blues were missing the influence of Cesc Fabregas:
With just two minutes of the first half remaining, Pedro cut inside from the left and saw his deflected shot cannon off the post.
However, Chelsea were not to be denied and eventually broke the deadlock in first-half stoppage time.
Hazard won a free-kick on the edge of the box, and Alonso curled it around the wall and beyond Forster.
Football writer Seb Stafford-Bloor felt goalkeeper Forster should have done better:
Goal's Nizaar Kinsella illustrated just how dominant Chelsea had been in the first 45 minutes:
Southampton struggled to trouble Chelsea after the break and sent on in-form striker Charlie Austin to increase their attacking threat.
The striker almost scored with his first touch, after Nathan Redmond played him in, but his effort was tipped around the post by goalkeeper Thibaut Courtois.
Chelsea responded immediately to that warning as Hazard and Fabregas combined in the box, with the Belgian slotting home only for the offside flag to deny him.
Conte then sent Morata on for Hazard, and the substitute was quickly into the thick of the action, but Forster blocked his close-range shot.
With Chelsea having been unable to make the game safe, Southampton began to press in the closing stages, with the influential Austin testing Courtois once again.
Journalist Dan Levene said it made for a tense finish at Stamford Bridge:
Conte's side managed to hang on for all three points and a narrow victory. The hosts may feel they could have won by more, but some poor finishing let them down, and they endured some nervy moments particularly after Austin's introduction.