Italy were on top from the first whistle, and came close to taking the lead inside the opening minute when Ciro Immobile struck an effort just wide from the edge of the box.
Despite being forced onto the back foot for long spells, Malta could have been ahead had Clayton Failla's deflected shot crept into the bottom corner.
The visitors would improve as the first half progressed, but there were signs that it could have been a frustrating evening as Pelle and Giorgio Chiellini both hit the woodwork with powerful headers.
However, it was Pelle who made the breakthrough as the Southampton striker took advantage of confusion inside the Malta box to fire home his first international goal.
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Immobile would go close once again a few moments later as his header from close range tested the reactions of Andrew Hogg in the Malta goal.
However, the hosts were unable to apply any pressure on Italy, who looked comfortable in the closing stages as they secured all three points.