Argentina-born Retegui scored on his international debut in the 2-1 defeat to England and found the net once more with a simple 15th-minute opener three days later.
Matthew Guillaumier's own goal 12 minutes later offered Roberto Mancini's side complete control at Ta' Qali National Stadium, with Malta rarely threatening a response.
Victory leaves Italy three points behind embryonic Group C leaders England, which eased past Ukraine by the same scoreline earlier in the day.
Malta almost grabbed an unlikely fifth-minute lead but captain Gianluigi Donnarumma rescued Italy with a fine stop against Alexander Satariano when one-on-one.
That missed chance proved pivotal as an unmarked Retegui headed home from Sandro Tonali's corner soon after, before Wilfried Gnonto limped off injured.
Guillaumier turned into his own net from Emerson's inviting cross as Italy furthered their lead, though Henry Bonello denied substitute Vincenzo Grifo to keep the scoreline respectable at half-time.
A frantic scramble inside the Italy area offered Mancini's visitors a rare second-half scare before Bonello thwarted a fizzing Bryan Cristante attempt.
Gianluca Scamacca's inventive acrobatic effort forced another smart Bonello save as Italy cruised to their first win on the road to Germany 2024.