Lampard converted a penalty after Jussi Jaaskelainen upended Oscar when trying to meet Guy Demel's dreadful back-pass, with the Finland goalkeeper fortunate to stay on the field.
Oscar added a second before the break for Jose Mourinho's men and Lampard scored his second late on with a trademark effort from the edge of the area to extend West Ham's winless home run to five matches.
The strikes were Lampard's first Barclays Premier League goals since the opening day of the season, ending a 10-match scoreless run, as he took his tally to five goals in his last five league appearances against the club he left in the summer of 2001.
The Hammers, who have now failed to score in seven of their 11 league matches this season, had won once since the opening day defeat of Cardiff, 3-0 at Tottenham when their strikerless style was employed to devastating effect.
Since the Spurs success, West Ham have claimed two points in four games, yet once again Sam Allardyce went without a recognised striker against a Chelsea side bidding to end a two-match winless streak in the Premier League, something of a crisis for the Blues.
West Ham claimed a 3-1 win in the same fixture at Upton Park last season and started brightly, but it was Chelsea's attacking quartet of Samuel Eto'o, Eden Hazard, Oscar and Ramires - deployed further forward with John Obi Mikel drafted into defensive midfield - who always looked dangerous.
Ravel Morrison, who terrorised Tottenham, was prominent early on before Chelsea went in front through a terrible Hammers error.
Demel failed to deal with a harmless-looking lofted ball into the area, playing the ball weakly with his thigh back in the vague direction of Jaaskelainen.
Oscar nipped in and the goalkeeper dived at the feet of Brazilian, only to fell the Chelsea forward and concede a penalty.
Referee Chris Foy opted not to dole out further punishment when Jaaskelainen might have been dismissed for denying a goalscoring opportunity and Lampard stepped up to blast the spot-kick into the net.
The 35-year-old headed a yard wide from Hazard's cross as Chelsea threatened again before doubling their advantage when Hazard flicked the ball on for Oscar, who did the rest.
Unchallenged, Oscar surged forward and slotted a low shot into the bottom corner.
Cesar Azpilicueta, who was again preferred to Ashley Cole at left-back, was targeted as a weak link and time and again Stewart Downing fired deep crosses to the back post, but the Spaniard repeatedly dealt with the danger.
Allardyce turned to his replacements five minutes before the break and replaced Jack Collison with Madibo Maiga, a striker, and Joe Cole with Mohamed Diame, who scored in last season's fixture.
The decisions were met with derision and cries of 'You don't know what you're doing'.
Eto'o had a curling effort from inside the left edge of the box saved before Azpilicueta snuffed out a counter-attack by Morrison.
Chelsea resumed intent on adding to their lead and Gary Cahill had a header hacked off the line by Mark Noble from Lampard's corner.
The midfielder then had a shot through Joey O'Brien's legs saved and Oscar fired wide from Azpilicueta's cross when he should have hit the target.
Maiga was unable to connect cleanly with an acrobatic effort as the Hammers' struggles continued and Eto'o curled a shot narrowly off target when the home defence allowed him to turn.
West Ham's lack of luck was summed up when Demel shrugged off Azpilicueta and Hazard by the corner flag and lost Lampard in the area, only to see his cross prodded wide by Maiga at the far post.
It was the Hammers' best chance of the match.
Chelsea's third soon followed.
Branislav Ivanovic crossed, Hazard had a shot blocked, but only as far as Lampard, who hit a low shot into the bottom corner beyond Jaaskelainen.
The Finn has now conceded 49 goals in 22 Premier League games against Chelsea and is still to keep a clean sheet.
Lampard celebrated by kissing the Chelsea badge on his shirt.
Michael Essien had an effort saved after being teed-up by fellow substitute Andre Schurrle as Chelsea sought a fourth.
Another replacement Demba Ba, who scored seven goals in 12 Premier League appearances for West Ham in a six-month spell in 2011, found the net in stoppage time only to be ruled offside as the visitors had to settle for three in a convincing win which sees West Ham worryingly looking over their shoulders.