Frank Lampard's penalty after three minutes silenced the crowd and England had their first three Group H points in the bag before half-time with Lampard heading a second and Jermain Defoe's shot underlining the gulf in class between the sides.
England's tempo dropped after the break as Moldova enjoyed a little more of the ball but the hosts conceded twice more late on as James Milner and Leighton Baines scored their first goals for their country.
Roy Hodgson's side will expect a tougher task against Euro 2012 co-hosts Ukraine at Wembley on Tuesday but the manner of their opening victory, albeit against lightweight opposition, will provide grounds for optimism for the qualifying campaign.
"The key was the start," Lampard, whose opener was England's 100th penalty in international football, told ITV Sport.
"It can be tough coming to places like this and we were expected to win. But the way we started showed our intentions tonight and we were comfortable at half-time."
England enjoyed the perfect start when Moldova's Simion Bulgaru inadvertently blocked Manchester United midfielder Tom Cleverley's shot with his flailing arm and Lampard stepped up to bury his spot-kick low into the corner.
The midfielder showed his scoring instincts again after 29 minutes, collecting his 25th England goal when he guided a firm header beyond Moldova keeper Stanislav Namasco from Glen Johnson's inviting cross.
"My only concern is the injury to John Terry," Hodgson said. "I don't think it's a very serious injury, but Tuesday is very close. I will have to wait and see what the doctors tell me."
