Much of “The Last Romance” takes place in a dog park, a setting that reflects the dogged nature of its main character, 80-year-old widower Ralph Bellini, as he pursues an initially reluctant woman, Carol Reynolds, whom he first noticed walking her Chihuahua.

At this point you think you know how things will turn out in this bittersweet comedy, but hold that thought. Playwright Joe DiPietro (“I Love You, You’re Perfect, Now Change,” the Broadway musical “Memphis”) sometimes writes New York Times Sunday crossword puzzles and that requires a heap of unpredictability lest readers get bored and turn the page.

Nobody’s going to get bored with the script or with Michelle Mountain’s production at Purple Rose Theatre. DiPietro’s three-hander (the third being Ralph’s housemate, cook and sister, Rose) strikes an all-too-rare balance of plot and character: Things happen, they happen because of the way people behave, and each character is uniquely flawed and uniquely admirable. Almost immediately you want to know about them, and once you do you want to find out what’s going to happen. You can’t ask for much more in an evening of theater.

They have regret and loneliness in common (but it’s a comedy, really) and, just to extend the canine metaphors, you might say that Ralph is a terrier who latches onto something and won’t let go, Rose is a loyal bloodhound who assumes the role of being her brother’s keeper, literally, and Carol is like her own timid dog.

Mountain’s actors serve the script exceptionally well. Will David Young is all charm and twinkle from the moment he attempts to initiate conversation with Carol by asking “Do you like opera?” But there is an ever-present undercurrent of disappointment in Young’s demeanor. It has to do with opera, and the story is among the many revelations DiPietro will provide.

Franette Liebow portrays well Carol’s conflict between self-imposed diffidence and undeniable attraction to the handsome man on the park bench. Carol is the character who changes the most as things progress, and Liebow negotiates that with skillful subtlety.

Priscilla Lindsay turns in a thoroughly natural performance as Ralph’s divorced sister, Rose, whose bossy intrusiveness is how she expresses loyalty to and concern for her brother. Additionally, she’s jealous of Carol, afraid that her brother will leave her for this interloper. Lindsay conveys these emotions by the way she nearly stomps when she walks and even when her back is to the audience by the way she stands.

A real live dog puts in a relatively brief appearance, an adorable little Chihuahua (two of them alternate in the role) who steals its scenes. If DiPietro has any brains, the human actors say nothing of consequence while the four-legged actor is onstage. I couldn’t tell you because all my attention was on the dog.

Also alternating in one role are Andrew Buckshaw and Ryan Dooley who play a character called The Young Man who sings arias between scenes. He represents a younger or alternative Ralph, although that’s open to interpretation.

Reid G. Johnson supplies atmospheric lighting, mostly the late afternoon, outdoor variety, and Rhiannon Ragland’s costumes ideally suit the characters: dapper for Ralph, subdued with flashes of color for Carol, dowdy for Rose.