The Belgian had been lively for the opening half an hour, and his goal was the culmination of his performance.
The move for the goal started when Ross Barkley showed why he had recently been recalled to the England squad.
The midfielder dispossessed Southampton's Hojbjerg in a dangerous position, before playing a good through ball to Hazard.
All that was left was for the Premier League's top goalscorer to fire a fine finish past Alex McCarthy in the Southampton goal.
It was Hazard's seventh goal of the season in just his eighth game in the Premier League.