Lampard came on for the injured Ramires in the 24th minute and had the major impact on the game.
David Luiz's presence in midfield allowed the England international to push forward from deep and he fired in a 25-yard shot which Michel Vorm turned around the post.
The veteran then provided the assist for Oscar's 43rd minute opener. The goal came after John Terry intercepted a long ball forward before striding purposefully into midfield. He fed Lampard, who in turn found Oscar, and the Brazilian drilled a shot across goal inside the far post.
The Blues doubled their advantage in first-half injury-time after Juan Mata combined with Eden Hazard before being pulled down by Leon Britton in the box.
Lampard stepped up to notch his 201st goal for the club from the spot - one short of Bobby Tambling's Chelsea record.
Tambling was introduced on the pitch at half-time and saw Chelsea begin the second half well.
There were also a few moments of worry when Michu and Wayne Routledge escaped the attentions of Terry, only for the hosts to survive.
At the other end last season's European champions were unable to add to their total, with Demba Ba having the best chance of the half but Vorm did well to push his shot away.
Mata also came close to a goal on his 25th birthday but his shot across goal went narrowly wide and was just out of the reach of Ba's outstretched leg.
The win sees Rafael Benitez's side move three points clear of rivals Tottenham in the battle for a place in the Premier League top four and extended Swansea's winless run to six games.