THERE: To the end, Mirren’s Jane Tennison gives us what we wanted.

When Detective Jane Tennison made her 1992 debut on PBS’s Mystery!, she wasn’t the first female cop on television to stare down murderers. Angie Dickinson’s toothsome Police Woman and CBS’s groundbreaking Cagney & Lacey had put women on the force. But Prime Suspect, written by Lynda LaPlante as an answer to the many all-male police procedurals on British TV, finally put a woman in charge. Fifteen years and seven telefilms on, Tennison is now a detective superintendent on the verge of retirement, but the job has been hard on her soul. Even so, she doesn’t seem ready to quit.

Prime Suspect: The Final Act (airing in two parts, November 12 and 19, on WGBH Channel 2 at 9 pm) begins with the discovery of not a dead person but a semi-conscious one: the heroine herself, hung over and disheveled, waking in a strange place that turns out to be her own house. Ever the professional, she staggers to the office — after downing another drink. Like many high-functioning addicts, Tennison looks fine. At 60, she’s got a personal style (and a stylish, no-iron blouse/skirt set) that works double overtime. But look closer: her long-time habit is in her bloodshot eyes and unsteady hands. That her junior staff lets it slide speaks to how respected (or feared) she is. Or perhaps it demonstrates how youth tends to avoid those with a one-way ticket to Florida. “Where all the old coppers go now,” she says bitterly.

What a change from when we first met Jane Tennison and she was all sharp elbows and crackling nervous energy. Charging after pedophiles, drug kingpins, and serial rapist murderers, she was usually on the right track even if she rattled a few cages along the way. Mirren has said that she’s always enjoyed playing Tennison’s “unlikability.” And Jane is certainly difficult to get on with: she alienated one lover, a fame-seeking forensic psychologist/author (Stuart Wilson), and another, a junior detective (Colin Salmon), became “a distraction.”

LaPlante, who wrote the first three installments of Prime Suspect before moving on, has said that she’s disappointed in how her most famous character turned out: “I just find it very sad that for the end of a great character, female, somebody has to say, ‘Make her a drunk.’ ” In truth, it’s Tennison’s struggle with alcohol that gives The Final Act its power. It was LaPlante herself who originally wanted realistic, hard-driving, hard-drinking, chainsmoking cops. It figures that there’d be a few casualties. And Tennison’s not alone: one of the finale’s grace notes is the reappearance of DS Bill Otley (the late Tom Bell), the snide sexist who nearly shipwrecked her first murder investigation.

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The solution to the murder mystery itself doesn’t come as a surprise. There’s a missing schoolgirl with a secret life, and the likely suspects announce themselves early on. More haunting is the surreal scene in which Tennison arrives — late, of course — at the funeral of someone close to her. Watching from across a city street, she sees the hearse draw up at the church doors, and everything’s beginning and ending without her. The pitiless urban traffic won’t let her cross over and join the mourners.

Don’t worry, the story doesn’t end there. Under the worst circumstances, Tennison often manages a strange kindness. To a small girl who’s pointing a loaded gun at her, she asks sweetly, “You’re not going to take that to school, are you?” Works like a charm. But watch out for her “gentlewoman next door” voice. Later on in The Final Act, she summons the same tone to extract a statement from a suspect. Is she showing true compassion or understanding? Does it matter? The moment she’s done, she snarls at a colleague, “There. You got what you wanted.” Prime Suspect ends without compromising its difficult heroine. Jane Tennison gets what she most wants: a chance to do her job. She solves the crime. And she closes the case.