The functional response and predation parameters of three species of predatory pirate bugs Amphiareus constrictus (Stal), Blaptostethus pallescens Poppius, and Orius tristicolor (White) (Hemiptera: Anthocoridae) were evaluated at four different densities of eggs of Tuta absoluta (Meyrick) (Lepidoptera: Gelechiidae). Experiments were conducted in Petri dishes containing a tomato leaf disk infested with the pest eggs, and maintained inside growth chamber with environmental conditions of 25±2°C, 70±10% relative humidity, and a photoperiod of 12:12 (L:D) h. A. constrictus and B. pallescens showed a type III functional response where predation increased at a decreasing rate after egg density was higher than 12 per leaf disk, reaching an upper plateau of 18.86 and 25.42 eggs per 24 hours, respectively. By contrast, O. tristicolor showed a type II functional response where the number of eggs preyed upon increased at a decreasing rate as egg density increased, reaching an upper limit of 15.20 eggs per 24 hours. The predator equations used in this study estimated handling time of 1.25, 0.87, 0.96 h for A. constrictus, B. pallescens, and O. tristicolor, respectively. The lower handling time and possible higher attack rate of B. pallescens suggests a higher efficiency and probably greater impact on the pest population. If conservation or classical biological control of T. absoluta is to be implemented, then prioritizing which natural enemy species is the most efficient is an important first step.