Defending champions Spain, seeking an unprecedented third triumph, also started with a hard fought 1-0 win over Czech Republic. Zlatani Ibrahimovic's Sweden and Irish Republic drew 1-1.
Belgium's Red Devils were punished by a ruthless Italian performance despite dominating for long spells of the Group E clash in Lyon.
Italy's coach said the team's first round failure at the 2014 World Cup should inspire the Azzurri to success at the European Championship.
Giaccherini's strike just after the half hour put future Chelsea manager Conte's men in front before Southampton striker Pelle sealed the win with a thumping finish from Antonio Candreva's cross.
Veteran goalkeeper and captain Gianluigi Buffon sprinted the length of the pitch to join in the celebrations. Pelle also jumped as though he had won the tournament.
Belgium now face a crucial clash with Ireland on Saturday in Bordeaux if they are to avoid an embarrassing early exit.
A star-studded Belgian attack containing Eden Hazard, Kevin de Bruyne and Romelu Lukaku were frustrated throughout by Italy's 'BBC' defence of Andre Barzagli, Leonardo Bonucci and Giorgio Chiellini.
At the other end, the Belgians were exposed when Bonucci's long floated pass found Giaccherini in behind the Belgium defence to stroke his shot past the exposed Thibaut Courtois.
Belgium upped the intensity after the break and twice came close when Lukaku clipped the post before his replacement Divock Origi headed over when unmarked from close range.
But Italy continued to pose a threat on the counter-attack and sealed a massive three points when Pelle volleyed into an unguarded goal from Candreva's unselfish cross.
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