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.
Admittedly, the idea of the 45-year-old making an immediate leap from Florencio Varela to Stamford Bridge is rather far-fetched, even if in absolute terms he would enter the job with more experience than Lampard's sole season at Derby County behind him.
Crespo is still in the apprenticeship phase of his career on the bench, which is now taking wind after a rocky start.
The former Chelsea, Inter, Parma and Argentina striker received his first, brief taste of life as a coach at Serie B side Modena back in 2015, lasting less than a year in the post.
He went on to take the reins at Banfield in his native Argentina but despite a promising start filled with goals and excitement, results failed to match expectations and he was sacked in September 2019, making way for club stalwart Julio Cesar Falcioni.