London - Marco Alonso's free-kick on the stroke of half-time gave champions Chelsea their second Premier League win of the week with a 1-0 victory over Southampton on Saturday.
The hosts dominated but could not find a second against a Southampton team that defended resolutely, and needed a good save from goalkeeper Thibaut Courtois to deny Saints substitute Charlie Austin.
Chelsea's win saw them move into third place, 11 points adrift of leaders Manchester City, who were hosting Tottenham Hotspur in the late match.
Chelsea manager Antonio Conte -- who after last Saturday's loss to West Ham United all but ran up the white flag on their hopes of successfully defending their title -- resisted the temptation to bring Alvaro Morata into the side even though the striker had recovered from a back problem.
Little was seen of Chelsea in attack until the 14th minute when Willian cut inside and exchanged passes with Alonso but shot a yard wide.
Southampton goalkeeper Fraser Forster was not called into action until the 20th minute, when he had to push away a bouncing volley by Alonso and was fortunate a minute later when he could only parry a shot from distance by Gary Cahill but no Chelsea player was close enough to profit.
Forster did much better shortly afterwards when Hazard rolled the ball into the path of N'Golo Kante, whose deflected shot appeared to be on its way into the top corner of the net until the goalkeeper leapt to his right to touch the ball away.
Pedro went close to breaking the deadlock for Chelsea as half-time neared, forcing his way past a challenge and hitting a low shot that struck the base of the post.
Southampton's massed defence was making it hard for Chelsea despite the trickery of the home side's forwards, but one challenge too many proved their downfall.
Maya Yoshida was booked for a late tackle on Hazard and Alonso curved the free-kick around the wall and past the right hand of the diving Forster.
Courtois kept the hosts ahead on the hour mark, diving alertly to his left as Austin ran onto a pass from Pierre-Emile Hojbjerg and swerved a shot towards the corner.
Chelsea too pressed for a second, with the impressive Forster denying Alonso his second of the match after the left-back had chested down Willian's pass and volleyed with his right foot.
Morata, on as a substitute, shot too close to Forster and Alonso headed wide, while Cesc Fabregas caught out the defence following a quickly-taken free-kick, but his shot rolled across the face of the goal instead of into the net.