Oscar was awarded a penalty after being brought down by Jussi Jaaskelainen following a poor Guy Demel back-pass which Lampard converted on 21 minutes.
The Brazilian then doubled the advantage on 34 minutes following an Eden Hazard pass.
In the second period, Mark Noble cleared a Gary Cahill header from a corner off the line before Lampard put the game to bed with a low strike with eight minutes remaining to get the Blues' title charge back on track.
The defeat extended West Ham's winless home run to five matches and Sam Allardyce's side have now failed to score in seven of their 11 league matches this season, having won just 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, the Hammers have claimed two points in four games, yet once again Allardyce went without a recognised striker.
The hosts started brightly, but it was Chelsea's attacking quartet of Samuel Eto'o, 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 to Jaaskelainen 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, surging forward and slotting 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 Spain right-back 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. The decisions were met with derision and cries of 'You don't know what you're doing'.
Eto'o had a curling effort well saved by Jaaskelainen before Azpilicueta snuffed out a counter-attack by Morrison.
Chelsea resumed intent on adding to their lead and Cahill had a header hacked off the line by Noble from Lampard's corner.
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.
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 at the bottom of the table.