- Giacomo Bonaventura (22')
- Domenico Berardi (45'+1', 63')
- Davide Frattesi (90'+3')
The European champions had few problems at the Stadio San Nicola in Bari, despite contending with injuries, against a Malta side without a win so far in the qualifying campaign.
Italy's win leaves them in second place ahead on goal difference of Ukraine, who won 2-0 against North Macedonia. Both teams have 10 points but Italy have a match in hand on all their group rivals except England, who top the group with 13 points.
England host Italy in their next qualifier on Tuesday.
Giacomo Bonaventura opened the scoring after 23 minutes, netting his first international goal with a skillful right-foot curler into the top corner from just inside the penalty area.
At 34 years and 53 days, midfielder Bonaventura became the oldest Italy player to score his first goal for the national team - more than 10 years after his debut.
"Sorry it took so long, I got there eventually," he told Sky Sports Italia. "I was lucky, it went well ... these games against a very defensive team are tough to open the scoring."
Berardi increased Italy's lead with a left-foot curler just before halftime and added his second goal in the 64th minute with a precise finish from a cut-back.
In the closing moments, Davide Frattesi scored the final goal of the night, skillfully slotting a low shot from the edge of the area into the bottom corner.
Spalletti praised his side for their determined approach to the match against the group minnows.
"The important thing is the three points, never letting it be in doubt, without taking this test lightly, showing a professional attitude," Spalletti told RAI Sport.
"You can see these players are eager to get to know each other more and play good football, so we are pretty pleased."
Italy face England at Wembley Stadium on Tuesday when a win would put them level on points with Gareth Southgate's side, who will themselves clinch a place at the finals with a victory.
"That is a match where we can really see what our potential is. Once we have played, then I'll tell you what that potential is," added Spalletti.
- Duje Strukan