On his 595th Chelsea appearance, Lampard headed in an Eden Hazard cross after 19 minutes to move within two of Bobby Tambling's club record of 202 goals.
The impressive Hazard netted a second after 50 minutes as Chelsea moved a point above Tottenham, with a game in-hand, in the race for a Champions League qualifying place.
"It is one of my best days," Lampard told the BBC.
"Obviously, winning the Champions League and championships are the best, but personally getting 200 goals for the club, I never thought I would touch that so I am pleased to get it.
"Everyone keeps talking about the goalscoring record, I would rather people kept quiet. The important thing is trying to score goals to win games.
"We are in good form and everyone is at it. There is a good feeling around the place and we need to carry it on until the end of the season."
Lampard, who joined Chelsea from West Ham for £11million in 2001, celebrated his 12th league goal of the season in front of the away end and with John Terry, who was warming up as a substitute, with the visiting support expressing their displeasure by hurling objects the duo's way.
The Metropolitan Police later confirmed they were investigating incidents of coin throwing but that no arrests had been made.
Chelsea interim boss Rafael Benitez absolved Lampard of blame for celebrating in front of the visiting fans and was uncertain if any of his players had been hit by objects.
"When you score 200 goals you don't think too much about where you go," Benitez said.
"You celebrate and afterwards we realised he would've been better to be in another part."
Benitez confirmed fourth official Howard Webb advised the Chelsea substitutes to warm up at the other end after the goal.
Benitez declined the opportunity to compare Lampard and Steven Gerrard, his former captain at Liverpool.
He praised the team-mates that allow Lampard to get forward into the box and expressed a wish that the England international continues to find the net in the closing stages of the season.
"We have a lot of games to play," Benitez said.
"Hopefully he can score more goals. Hopefully he can score 15, 20 goals and he will be happy and I will be happy."
Due to his prior association with Liverpool, Benitez was an unpopular appointment for Chelsea.
But the hostility at Stamford Bridge towards Benitez appears to have reduced sufficiently that the usual jeering did not take place.
"If the team is playing well, the fans will enjoy it," said Benitez, who railed against the supporters following the FA Cup win at Middlesbrough, urging them to back the team.
"I'm really pleased with the atmosphere and really pleased with the team."
The international break offers brief respite for the Blues before the season resumes in earnest with six games in 16 days, beginning at Southampton on March 30.
Defeats this weekend for Manchester City, who are four points above the Blues in second, and Tottenham favoured Chelsea in their quest for a top-four spot.
"It's good, but you cannot influence the other results," Benitez said.
"You have to concentrate on your results, winning games. After we will see where we are in the table."
West Ham were second best throughout, but did have the ball in Chelsea's net, but Andy Carroll's strike was chalked off for a push in the back on David Luiz.
Hammers manager Sam Allardyce said: "Technically it was a foul, but I can show you about four of them outside the box he (referee Michael Oliver) didn't give.
"It was a brilliant dive by David Luiz and I think that bought him the foul.
"We were always in the game if we could score, but this year away from home scoring has been a massive problem for us.
"We had enough opportunities to score at least one today [Sunday]."
Allardyce praised Chelsea and Lampard.
"Sometimes you can't defend against the quality they've got," he said.