Argentina were without captain Lionel Messi for the second consecutive match, with a foot injury sidelining the 97-cap veteran, but Pastore stepped up in his absence.
Pastore netted the winner 13 minutes into the second half to inspire Argentina, ending his 17-match international goal drought.
Argentina and Ecuador were level at the break after Miller Bolanos cancelled out Sergio Aguero's eighth-minute opener in the United States.
Gerardo Martino's Argentina have one more friendly fixture - against Bolivia on June 6 - remaining before the Copa America kicks off in Chile in June, while Ecuador face Panama (June 3 and 7) in a double-header ahead of the tournament's curtain-raiser on June 11.
Argentina wasted no time asserting their dominance, with Aguero - unmarked at the back post - heading home Di Maria's corner from close range in the eighth minute for his 23rd goal in 60 appearances.
Marcos Rojo and Di Maria both came close to doubling Argentina's lead but Ecuador started to take control of proceedings from the 18th-minute mark after Mena's glancing header was dealt with by goalkeeper Sergio Romero.
Argentina almost regained the lead five minutes before half-time, when Lucas Biglia's free-kick bobbled up off the ground and forced Alexander Dominguez to spoon the ball away for a corner.
The second half began frantically, with Argentina's pace causing Ecuador problems and it was not long before Martino's men hit the front again.
