Italy, without a win in their previous four matches, struggled to find a way through a massed Maltese defence in front of a sparse crowd at the Artemio Franchi stadium.
The win took them top of Group H with 15 points from seven games, one more than Croatia who drew 0-0 in Azerbaijan earlier on Thursday.
Pelle, who scored the only goal when Italy won by the same score in Malta earlier in the group, was in the thick of the action for Italy as he had a shot deflected over the crossbar and headed over from a corner early on.
Malta, bottom of the group with one point, nearly took a sensational lead just before the half hour when Alfred Effiong curled a shot just wide of Gianluigi Buffon's far post.
As Italy continued to press forward, Pelle headed wide from an Andrea Pirlo free kick and then Malta goalkeeper Andrew Hogg did well to parry away Andrea Bertolacci's deflected shot.
Eder had Italy's best first-half effort when his low effort went just wide of the post after a run from midfield.
Malta continued to defend tenaciously after halftime and Italy struggled to create openings despite their overwhelming dominance.
Manolo Gabbiadini was agonisingly close to the breakthrough when he curled a 20-metre effort against the crossbar in the 59th minute, and Malta finally capitulated 10 minutes later.
Antonio Candreva sent over a cross from the right, Hogg was distracted by Marco Parolo at the near post and Pelle forced the ball in from close range.
Even after the goal, Malta continued to defence doggedly and Hogg did well turn away an awkward shot by Marco Parolo.
(Writing by Brian Homewood in Berne; Editing by Mike Collett)
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