The Italian, who missed last week's loss to Central Coast Mariners with a hamstring injury, ignited a dour first half with a brilliant individual goal in the 43rd minute before Ranko Despotovic made it 2-0 on the stroke of the interval.
But there was no sign of Del Piero after the break, with Brett Emerton making his return from a leg injury in place of the skipper.
Harry Kewell was introduced for the Heart in the 57th minute and missed a penalty nine minutes later after Joel Chianese handled the ball in the area.
The Australia veteran atoned when he was involved in the lead up to Michael Misfud's 72nd-minute goal as the Heart cut the deficit to 2-1.
But the hosts, who sit third, claimed the points to make it five wins from their last six league games, while Melbourne remain rooted to the foot of the table.
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