Lampard headed in the opening goal through Eden Hazard's cross to move within two goals of Bob Tambling's club record of 202 goals. Hazard turned goal-scorer in the 50th minute to secure all three points for the Blues.
Three points means Chelsea moved above Tottenham in the race for Champions League qualifying spot after Spurs fell to a 1-0 defeat against Fulham at White Hart Lane.
Lampard, 34, on his 595th Chelsea appearance, was unmarked in the box and scored his 11th league goal of the season.
Chelsea are currently going through a busy schedule with their 53rd match of the season and their fifth this month. The Blues drew 2-2 at Manchester United, came back to win against Steaua Bucharest and jumped back to third place in the league.
The last time Chelsea played West Ham, the Hammers came back to win 3-1 at Upton Park.
Despite being close to breaking the clubs goal scoring record, Lampard's future at Stamford Bridge is uncertain with his contract set to expire at the end of the season. It is likely that Chelsea will offer a short-term one-year deal if Lampard accepts a wage cut.
Lampard joined Chelsea from West Ham United for £11million and has spent 12 seasons at Stamford Bridge winning three Premier League titles, five FA Cups, two League Cups and a Champions League title.