At the beginning of Rajiv Joseph’s new play, “Dakar 2000,” a guy who calls himself Boubs tells us the story we’re about to see is “almost entirely true.” Boubs, an abbreviation for Boubacar — the character is half Indian — allows that names and some places have been changed, and that some of “the boring parts” have been “snipped away. Some other stuff has been added to make it … theoretically more interesting.”    

It will emerge later that for Boubs, who narrates the play as a middle-age man, hiding his cards has become a professional asset. Mr. Joseph, whose previous plays include a Pulitzer Prize finalist, “Bengal Tiger at the Baghdad Zoo,” and two Obie Award winners, “Guards at the Taj” and “Describe the Night,” is teasing us as well: As a young man, the playwright served for three years in the Peace Corps in Senegal — which is exactly what the 25-year-old Boubs is doing when he reappears after the prologue.

Boubs’s adventures in that role, in the waning days of the last millennium — when Mr. Joseph was around the same age — form the plot of “Dakar,” a crisp, tasty thriller that, under May Adrales’s witty direction, provides a winning showcase for its two cast members.

Boubs is played, both during this main journey and in scenes that frame it, set 25 years later, by Abubakr Ali, whose whole presence changes as the character shifts back and forth in time. Playing the narrator, the actor speaks in a clipped, almost chilly manner that suggests jadedness; as the younger Boubs, he’s more earnest and excitable, and sweetly awkward at times.

From the moment that Boubs encounters the play’s other character, an older woman named Dina — at least, that’s what she says her name is — we sense that his naivete will be exploited. When the two meet, Boubs has just been in a car accident; he lands in Dina’s office at the Department of State, where she introduces herself as the deputy regional supervisor of safety and security for sub-Saharan Africa.

Dina is at first cheerfully solicitous, but her questions gradually become more interrogative; learning he may be in trouble, Boubs appeals to her sympathy and gets an opportunity to earn her trust and respect. Dina sees promise in the young man and a bond is formed, though her motives remain suspect, even — especially — as she seems to let her guard down.

Stage veteran Mia Barron gives Dina the right casual authority and earthy sex appeal. It’s easy to see how a younger man in a less powerful position could be intimidated and seduced by her. Yet to both actors’ credit, and Mr. Joseph’s, the relationship between the two never devolves into a simple game of cat and mouse; we see both Dina’s humanity and the younger Boubs’s capacity for guile, and how their different world views — his is more idealistic, naturally — are valid, given their experiences.

Tim Mackabee’s scenic design marks their progress stylishly, taking us from Dina’s tidy, functional office to a starlit rooftop (beautifully rendered with lighting designer Alan C. Edwards) to the luxury hotel where the play reaches its truly suspenseful climax — which isn’t of the nature you might expect.

“I know a lot of you think the world is in a really bad place right now,” the older Boubs muses toward the end. “Like end-of-times stuff, worse, way worse than Y2K.” With “Dakar 2000,” Mr. Joseph ponders how recent history has led us here, while managing to provide some zesty entertainment in the process.