Stephan El Shaarawy bagged a brace while Bryan Cristante and Domenico Berardi, with their first Italy goals, were also on target and Veaceslav Posmac put through his own goal to complete a dreadful night for the visitors.
Italy fielded an experimental line-up, with Caputo becoming their second oldest-ever debutant, but Roberto Mancini's side were still far too good for the visitors as they extended their unbeaten run to 17 games.
Cristante opened the scoring with an easy near-post header in the 18th minute and Caputo, who has spent much of his career in the lower divisions of Italian football, ran onto Cristiano Biraghi's incisive pass and scored with a clinical finish five minutes later.
Chinese-based El Shaarawy showed superb control as he collected Cristante's looping pass, beat his marker and flicked the ball into the far corner on the half hour for the third.
Moldova provided the fourth as Posmac, in trying to clear the ball for a corner, instead fired into the roof of the net and El Shaarawy added a fifth on the stroke of halftime, the first time since 1987 that Italy have scored five in a first half.
The visiting defence was better organised after the break but could not stop Berardi scoring at the far post in the 72nd minute.