Jordi Alba and Neymar took advantage of two sensational passes from the No. 10 to settle an uncompromising showpiece, after both teams had been reduced to 10 men.
The Sweden international netted a superb double to sign off from PSG in style, and was joined on the scoresheet by midfielder Blaise Matuidi and fellow attacker Edinson Cavani.
The Spaniard swept home Juan Cuadrado's cross to finally break the deadlock in a poor game at the Stadio Olimpico, as the Bianconeri toiled in the absence of some key players.
The German Cup final went to penalties for the first time since 1999, with the Brazilian scoring Die Roten's fifth penalty to hand Pep Guardiola's men the trophy.
Diafra Sakho's early goal gave the Hammers hope of a much-needed victory at Old Trafford, but the Sweden international levelled proceedings with an excellent header.
The Frenchman was again on hand off the bench as Arsene Wenger's men snatched a late draw, leveling the game after a Juan Mata opener.
The Poland international showed just how finely tuned his technique is on the training pitch with immense but casual control over the ball in just a pair of socks.