Those two strikes sandwiched Oscar's 34th-minute effort as Chelsea claimed their first Premier League win in three matches.
Lampard's penalty came after Guy Demel's underhit backpass let in Oscar, who was brought down by goalkeeper Jussi Jaaskelainen, before Oscar himself made it two with a low effort from the edge of the box.
Lampard doubled his tally late on, converting from the edge of the box after Jaaskelainen parried Eden Hazard's shot, leaving West Ham without a win in five league matches.
Both sides made one change from their previous outings a fortnight ago, Joey O'Brien replacing the injured Razvan Rat for the hosts, while John Obi Mikel came in for Willian in the Chelsea midfield.
After a scrappy start to the game, the visitors were gifted the lead midway through the half.
Under no pressure, Demel's weak backpass towards Jaaskelainen was seized upon by Oscar, who went to ground under the goalkeeper's sliding challenge, referee Chris Foy showing no hesitation in pointing to the spot.
Lampard stepped up and smashed the kick high into the roof of the net to end his longest run without a league goal for Chelsea.
Thirteen minutes later Oscar tormented the hosts again, the Brazilian picking up Eden Hazard's clever flick before driving forward and rolling the ball into the bottom left-hand corner from 20 yards.
Jaaskelainen produced a fine save to deny Samuel Eto'o three minutes before the break, flying high to his left to parry the Cameroon international's curling shot behind.
Chelsea started the second half strongly, Gary Cahill seeing his header cleared off the line by Mark Noble in the 52nd minute before Oscar turned Cesar Azpilicueta's cross wide shortly afterwards.
The hosts ought to have reduced the deficit in the 64th minute when substitute Mohamed Diame jinked past three defenders on the byline before his deflected cross ran to fellow replacement Modibo Maiga, but the substitute turned the ball a foot wide of the post from six yards.
As the game entered its final 10 minutes, Hazard tested Jasskelainen from an angle and the rebound fell perfectly to Lampard who made no mistake with a first-time strike.
Demba Ba saw an injury-time goal chalked off for offside but the points were already in the bag for Chelsea, who move up to third in the Premier League, while West Ham are just one place above the relegation zone.