Chelsea kept pace with the leading pack in the Premier League as they moved into fourth place with an impressive win at Southampton.
Southampton had plenty of the ball but could not find a way through a well-drilled Chelsea, who looked the more threatening and went close when strikes from Hazard and Diego Costa were saved.
Costa, however, beat Forster at full stretch with a wonderful curled effort from 22 yards.
Victory was Chelsea’s fourth in a row in the league – a feat they last achieved in April 2015 – and put them one point behind Manchester City, Arsenal and Liverpool.
Hazard is now getting back to his best. Eden Hazard was the 2014-15 Premier League player of the season during a campaign in which former Chelsea manager Jose Mourinho said the Belgian had outperformed Real Madrid forward Cristiano Ronaldo.
Hazard struggled to maintain those heights as he struggled last season – managing just four goals and rarely showing the pace and trickery that had made him such a threat.
He showed skill and power with his goal at St Mary’s, scoring in three consecutive Premier League games for the first time, then provided the pass from which Costa added Chelsea’s second.
Eden Hazard, while mainly operating down the left flank, he has shown that he’s a threat from all over the pitch. He also had more shots on target and made more key passes than any other player.
Chelsea were exposed defensively in consecutive league defeats by Liverpool and Arsenal this season but, since then, they have kept four clean sheets and scored 11 goals.
Manager Antonio Conte’s move to a formation with three centre-backs is helping his side look more secure at the back and threatening in attack.
The Italian also appears to have implemented the sort of defending for which his country is famous, as an organised Chelsea denied Southampton’s players any space in or around the penalty area and closed them down with aggression throughout.
“It’s OK having the shape but it’s about having the mentality of the players to go out and dig in and do the business when you need to.”
Southampton, whose most recent defeat at home in the league came against Chelsea in February, again had little answer to the Blues.
Saints had 55 shots on target this season before the game, but could muster only one on Sunday despite enjoying 55% of possession.
Southampton’s chances were fleeting and, when they did come, striker Charlie Austin put one header wide and another high.
Man of the match, Eden Hazard scored and assisted in the same Premier League game for the first time since April 2015 against Stoke
“But it’s difficult to play against this team when you concede a goal after a few minutes. They can play their game with a strong defence and counter-attack.
“It was difficult to find solutions. It’s a disappointment because we tried to play good football. We can do better.”
Chelsea boss Antonio Conte: “We knew today was a test against a strong side in good shape and form. It’s important to win games like this – people can increase their confidence and will to work and trust in the work.
“We created many chances. It’s the perfect game when strikers score and defenders don’t concede. The players deserved this; they work hard in training.
“When you see this type of game and commitment from your players, it’s fantastic for a coach.”
Chelsea have exactly double the number of points (22) that they had after 10 games last season (11)
Southampton have kept only one clean sheet in their past 11 home Premier League games (1-0 v Swansea)
Southampton are at home to Inter Milan for a 20:05 GMT kick-off on Thursday, 3 November before a league game at Hull City at 14:15 on Sunday, 6 November.
Chelsea host Everton in the 17:30 kick-off on Saturday, 5 November.