Roy Hodgson's team took control of the match from the outset and were awarded a penalty when Tom Cleverley's shot hit the hand of a Moldovan defender.
Lampard stepped up from 12 yards and calmly converted his effort past Stanislav Namasco to give the visitors an early lead.
England could have extended their lead inside the first 10 minutes but Jermain Defoe's weak finish was easily saved by Namasco after good work from Alex Oxlade-Chamberlain on the wing.
Oxlade-Chamberlain continued to threaten the home side's defence and was close to scoring his first international goal with an acrobatic volley that Namasco was forced to parry.
Moldova's supporters didn't have too much to cheer in the first period but a long range strike from Artur Patras did threaten Joe Hart's goal before flying just wide of the target.
England did double their advantage in the 29th minute when Lampard found space inside the area to meet Glen Johnson's cross with an accurate header.
The visitors scored their third goal just two minutes later through Defoe, with the striker collecting a pass from the dangerous Oxlade-Chamberlain before firing his shot past Namasco.
England continued to push for more goals towards the end of the first half but some desperate defending from Moldova ensured that the lead remained at 3-0.