Sassuolo forward Caputo was named in an experimental line-up - one devoid of any Napoli or Juventus players due to coronavirus restrictions - and made his mark in a dominant first half for the host in Florence.
Italy registered five goals in the opening 45 minutes for the third time in its history, Stephan El Shaarawy netting twice - either side of Veaceslav Posmac's own goal - after Bryan Cristante had opened the scoring.
Domenico Berardi scored the only goal of a quieter second half as Italy hit its stride ahead of important Nations League games against Poland and the Netherlands.
After Salvatore Sirigu had produced a good save to deny Ion Nicolaescu, Cristante opened the scoring with a glancing header at the near post.
Moldova is 163 places below its opponent in the FIFA rankings and that gap was made clear when Caputo coolly converted, having been played clean through by Cristiano Biraghi.
El Shaarawy controlled Cristante's pass and flicked it past Alexei Koselev for the third goal and Posmac - in an attempt to clear the ball - booted into his own net for the fourth.
Captain for the day, El Shaarawy had his second just before half-time, getting the final touch to the ball close to the line after Manuel Lazzari had lifted it over the onrushing Koselev.
Italy took its foot off the gas in the second half, not helped by a plethora of substitutions, but Berardi added another 18 minutes from time with a close-range finish after being teed up by Vincenzo Grifo.