Oscar put Chelsea ahead at Stamford Bridge in the 44th minute and Frank Lampard then doubled the lead from the penalty spot a minute later for his 201st goal for the club.
Lampard began the game on the bench but came on because of a thigh injury for Ramires and scored his 15th goal of the season.
The hosts' opener came after John Terry intercepted a long ball forward before striding purposefully into midfield. He fed Lampard, who in turn found Oscar, and the Brazil forward drilled a shot across goal inside the far post.
Chelsea doubled their advantage before the interval after Juan Mata combined with Hazard before being pulled down by Leon Britton.
Lampard fired the ball low into the right corner and immediately Stamford Bridge erupted into chants of "sign him up". The midfielder's contract expires after this season, and he has not been offered a new deal.
The last season's European champions were unable to add to their total in the second half as Rafael Benitez's side moved into third place in the Premier League, one point ahead of Arsenal and three clear of rival Tottenham in the battle for a place in the top four. Swansea extended its winless run to six games.
Chelsea's next Premier League clash comes at Manchester United before the London derby with Spurs on May 8 which could prove decisive in the Champions League qualifying race.
For now they remain on course to achieve their two remaining targets this term and they will seek to confirm their place in the Europa League final in Thursday's semifinal second leg with Basel.
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