The Southampton forward has hit the ground running since arriving in England, scoring five times in nine matches this season.
And Pelle - one of four changes from Italy's 2-1 win over Azerbaijan, replacing Simone Zaza - kept up his scoring form in the Group H clash, netting a close-range finish midway through the first half.
Malta's chances were significantly harmed when captain Michael Mifsud was given a straight red card for a dangerous challenge on Alessandro Florenzi in the 27th minute.
Italy coach Antonio Conte had urged his side to be more ruthless after toiling in their victory against Azerbaijan, but they were held back from further adding to their tally when Leonardo Bonucci was sent off for denying a clear goalscoring opportunity 17 minutes from time.
The result leaves Italy with a maximum return of nine points from three matches, while Malta have now lost all of their games.
The 35-year-old Andrea Pirlo was rested by Conte, but Italy were more than capable of coping in his absence against a side ranked 155th in the world, 142 places below them.
The visitors began brightly, and Ciro Immobile fired an early warning with a sharp turn and shot just off target inside the first minute.
Malta went close themselves on the quarter-hour mark, when Clayton Failla fizzed a low shot narrowly wide of the right-hand post after pouncing on a loose ball on the edge of the area.
Italy responded strongly and hit the woodwork twice in quick succession three minutes later.
First, Pelle met Manuel Pasqual's cross with a powerful header that thudded back off the crossbar before being hacked away and then from the resulting corner Giorgio Chiellini nodded Pasqual's delivery against the upright.
Italy did take the lead in the 23rd minute, though, as another Pasqual corner caused chaos in the Malta penalty area.
Bonucci's header was saved by Andrew Hogg but the loose ball found its way to Pelle, who tucked home from inside the six-yard box.
Things then went from bad to worse for Malta as Mifsud was dismissed for a studs-up challenge on Florenzi.
Antonio Candreva's mis-hit cross clipped the top of the bar in the opening minute of the second period, while Ryan Camilleri was perhaps fortunate not to concede a penalty for a push on Immobile inside the box.
Immobile then headed straight at Hogg from close range when he ought to have scored before the numbers were evened up when referee Ovidiu Hategan gave Bonucci his marching orders after he brought down Andre Schembri 40 yards from goal.
Italy replaced Pelle with Angelo Ogbonna in a bid to shore up their defence but it was another replacement, Sebastian Giovinco, who almost had a telling impact, striking the base of the post after racing clear.
It mattered little, though, as Italy ensured they maintained their perfect start to qualifying.
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