The Juventus centre-back charged in to score the winner for the world champions in the 28th minute after Giampaolo Pazzini nodded on a corner from the right.
Sweden, without Zlatan Ibrahimovic in their first game under new coach Erik Hamren, had made a bright start and Italy keeper Federico Marchetti twice showed sharp reflexes.
The hosts then came forward at pace and created several chances. Chiellini had a header deflected off target by Andreas Isaksson's chest before he found the net and he also forced a fine save just before half-time.
Palermo defender Mattia Cassani came on to make his debut for the Azzurri at the start of the second half, which was largely uneventful until Marchetti did well to repel a Pontus Wernbloom header in the closing stages.
"It was a satisfying match, attacks at both ends," Italy coach Marcello Lippi told Rai television.
"Even though it was a totally new team the lads did not feel the effects. They played with commitment, desire and enthusiasm."
Hamren is also in charge of Norwegian champions Rosenborg Trondheim at the moment, but in August he will take over the national team full-time following Lars Lagerback's resignation after Sweden failed to qualify for the World Cup.
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