In the search for the management of ticks Rhipicephalus (Boophilus) microplus in cattle farming, coumarins have been used. These compounds frequently are associated with acaricidal effects against the genus Rhipicephalus. Several simple coumarins were synthesized according to green chemistry procedures. A solvent-free protocol of coumarins by the Pechmann method using a bulk Preyssler heteropolyacid was employed. High selectivity and very good yields at short reaction times were obtained. These compounds were evaluated as acaricides on adult cattle ticks Rhipicephalus (Boophilus) microplus. The Cox regression was used to understand the coumarins biological activity. Besides, Docking molecular and Quantitative Structure-Activity Relationship (QSAR) studies of these coumarins were conducted to explain the acaricidal effect. Several synthesized coumarins exceed the effect produced by ethion on the survival of engorged females of this species. Thus, simple and green-synthesized coumarins containing these two conditions are promising insecticide candidates for R. (B.) microplus control which are easily obtained using the synthesis protocol proposed.