Sudamericana top scorer Braian Romero subsequently doubled Defensa's advantage in the second half when he took advantage of an error at the back from Lanus to net his 10th of the competition and effectively put the final out of reach.
Lanus pushed hard for a way back, but they failed to breach the Halcon's lines and Crespo's charges added another in the final minutes through substitute Washington Camacho for a 3-0 victory.
As well as marking the ex-striker's maiden crown, it is also the first title in Defensa y Justicia's 85-year history.
Crespo took over in Florencio Varela at the start of 2020 after a previous spell at fellow south Buenos Aires side Banfield.