We developed an intelligent tutoring system (ITS) that aims to promote engagement and learning by dynamically detecting and responding to students' boredom and disengagement. The tutor uses a commercial eye tracker to monitor a student's gaze patterns and identify when the student is bored, disengaged, or is zoning out. The tutor then attempts to reengage the student with dialog moves that direct the student to reorient his or her attentional patterns towards the animated pedagogical agent embodying the tutor. We evaluated the efficacy of the gaze-reactive tutor in promoting learning, motivation, and engagement in a controlled experiment where 48 students were tutored on four biology topics with both gaze-reactive and non-gaze-reactive (control condition) versions of the tutor. The results indicated that: (a) gaze-sensitive dialogs were successful in dynamically reorienting students' attentional patterns to the important areas of the interface, (b) gaze-reactivity was effective in promoting learning gains for questions that required deep reasoning, (c) gaze-reactivity had minimal impact on students' state motivation and on self-reported engagement, and (d) individual differences in scholastic aptitude moderated the impact of gaze-reactivity on overall learning gains. We discuss the implications of our findings, limitations, future work, and consider the possibility of using gaze-reactive ITSs in classrooms.