England's superiority was clear from the first whistle and they were given an opportunity to take the lead when Tom Cleverley's shot struck a Moldovan defender's hand.
Frank Lampard converted the penalty to make the early breakthrough and score his 24th international goal in the process.
The visitors could have been further ahead four minutes later but Jermain Defoe failed to make good contact with his close-range effort and Stanislav Namasco pushed the ball to safety.
Moldova rarely posed a threat to England's defence in the first period and Lampard proved the dominance of Hodgson's side when he doubled his tally for the evening in the 29th minute by losing his market to head home Glen Johnson's accurate delivery.
Cleverley hit the post with a long-range strike just moments later but it was Defoe who managed to score England's third goal inside the Zimbru Stadium.
The Tottenham Hotspur striker was picked out inside the box by the lively Alex Oxlade-Chamberlain and took advantage of the opportunity by firing his shot past Namasco at the near post.
The hosts had their best sight of goal on the stroke of half-time but a towering header from Igor Armas landed safely wide of Hart's post.
England were able to relax in the second half, with Steven Gerrard and Oxlade-Chamberlain both being take off to avoid the risk of injury but Hodgson's men continued to enjoy the lion's share of possession.
James Milner added a fourth for England with 16 minutes remaining by stroking his shot into the corner of the net after a good passing move that included Cleverley and Welbeck.
The scoring was completed in the 84th minute when Leighton Baines hit a free kick from 25 yards, with the ball taking a wicked deflection off the wall to beat Namasco for the fifth time in the match.