Luis Enrique's side looked to have sealed a win with two second half goals after Eden Hazard's solo strike, but Gary Cahill's header forced the game to penalties.
El Tri had struggled for fluency prior to the tournament but stormed to a victory in their Gold Cup opener against a side blighted by off-the-field difficulties.
After 120 minutes without a goal in the Copa America and it was the tournament hosts who emerged triumphant through a penalty shootout.
Los Incas struck twice after half-time to seal a third-place Copa America finish for the second consecutive edition of the tournament.
The Barcelona star didn't find the net but was at his creative best as Tata Martino's side cruised through to the Copa America final in Concepcion.
The Napoli-owned striker bagged two on the night, both opening the scoring and netting a superb winning goal.
Carlos Tevez netted the winning penalty to seal his side's place in the Copa America semi-finals after an astonishing shoot-out.
The Juventus full-back fired home with 10 minutes remaining to set up a clash with either Bolivia or Peru in the last four of the Copa America.