The current tour by Alanis Morissette and Garbage has been characterized as a “Jagged Little Pill” 25th anniversary tour, and as it so happens, Garbage’s self-titled debut album came out just a couple of months after “Pill” did, so it’s a silver jubilee all around. What this occasion also means is that this has to be roughly the 23rd or 24th anniversary of starting to take both Morissette and Shirley Manson too much for granted, rather than holding them in mind all this time as national treasures.

The pendulum has clearly swung back in the favor of their proper recognition, in any case, judging from the rapturous reception of a full house Tuesday night at the Hollywood Bowl, with a followup to come Wednesday. Part of it may be down to anniversary fever — who doesn’t love a good quadranscentennial? — and part of it due to Morissette’s higher profile, even on an opposite coast, as a result of the “Jagged Little Pill” stage adaptation’s successful Broadway run. But there was more than a little bit of a gathering-of-the-tribe feel for the mostly female, mostly 35-to-60 crowd. It was nostalgia night, and not just wistfulness for “Hand in My Pocket” but for a time when it seemed like women might always authoritatively rule the alt-rock roost. If we knew then what we know now, there might have been a lot more of these Bowl bills in the last 25 years. (Or 26, actually, the 25th-anniversary tour having been delayed by a pandemic year, but in a drought, who’s counting?)

Opening act Cat Power (performing solo as the substitute for the originally billed Liz Phair, who ducked out for personal reasons a couple months back) spoke briefly but incredulously to the mini-Lilith Fair aspects: “I’m not used to touring on women’s bills,” she said, with a sense of gratitude and understatement. Morissette, for her concluding part, didn’t have much to say at all during her set, letting the music do the talking.

But Garbage’s Manson gave a nearly five-minute speech about why she thought this was special. “I don’t want to exclude my male compatriots, because they’ve obviously been very important and I wouldn’t be up here without them … but there is enough made about male achievement in this world, so I want to talk a little about female achievement — yeah? Here we are and we have three generations of female artists who have somehow… negotiated a very very difficult music industry… It’s important that female artists support each other, and I’m so indebted to Alanis for showing such support to people like me, to people like Chan Marshall.” Manson even took the love to artists not on the bill, saying, “I want to give a big shout-out to Karen O who I love with a vengeance, who has done nothing support me behind the scenes with no fucking political reason behind it other than being just a cool girl doing cool things for cool artists. Women sharing experiences, wisdom and rituals is an amazing thing.” It was a 17,500-strong choir being preached to.

If the many incantatory moments in Morissette’s set had an almost pop-shamanistic feel, Manson was the electro-punk godmother to Alanis’ earth mama, bringing swagger and “Wicked Ways” to the stage as a setup for the headliner’s more spiritual bent. Garbage hasn’t necessarily evolved greatly over the last quarter-century, but that’s partly because she, Butch Vig and company got something right out of the gate that was built to last, with a combination of loud guitars, a somewhat programmed feel and pure snarl that set a template too few others have successfully followed. It’s not a bad thing that the songs off the band’s recent “No Gods No Masters” could have been on the ’95 debut, or vice versa: Hearing an electronic pulse following by a crashing guitar riff won’t wear out out anytime soon, and Manson won’t run out of gods or patriarchies to have a bad attitude about in the next 25 years, either, even if she does pack a whole career’s worth of cheerful F-words into a single performance.

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Garbage at the Hollywood Bowl Chris Willman/Variety

After Manson appeared in a smart yellow jacket, the high-fashion part of the evening was over, as Morissette came out in a Black Cat T-shirt, as if advertising firecrackers, which would not be false advertising. Although “You Oughta Know” was inevitably the pre-encore closer to her 90-minute set, what became abundantly clear in the run-up to that is what an outlier that has been in her career. Did she disappoint some part of the world by not expanding and exploiting thatin that into a career-long angry-woman trope? It’s possible. But her catalog was made richer by keeping that as the flavor it was always meant to be, with her wail even more suited to bittersweet soul-searching than short-form vengeance. She has one of the greatest voices in rock — so powerful a voice, it seemed as if her pulling her head back from the mic was like an involuntary response to a constant series of rifle discharges, even if it was just a pro carefully working the dynamics. It’s too great and soulful a voice to have ever wasted on pure rage… although when that comes, too, toward the end of the show, it’s sure fun.

The bulk of the material came from “Jagged Little Pill,” naturally, and what remains besides the then-teen’s preternatural maturity in writing that going-on-50 material (along with Glen Ballard) is how mind-blowingly good some of the chord changes in those early songs are, from the gentle folk-pop “Head Over Feet” to a song that would be high in the Led Zeppelin catalog if it’d been just a little heavier, “Uninvited.” Actually, on this tour, her band is taking the implicit rock in some of those songs and making it more explicit — this is an outing that merits an eventual live album for anyone who might have ever wished the early material rocked just a little harder. Her latest album, 2019’s “Such Pretty Forks in the Road,” is quieter and more piano-based, but she mined it effectively for two of the better songs in the set, the pungent “Reasons I Drink” (accompanied, like a number of songs in the show, by videos of interpretive dancing) and “Smiling,” which built up enough broodiness to make for an ideal, penultimate lead-in to “You Oughta Know.”

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Alanis Morissette at the Hollywood Bowl Dennys Ilic

Other thoughts from the show: With songs this good, from one of the best debut albums of all time, who gives a shit about textbooks definitions of irony, anyway? Morissette took a lot of flack in the day for being too earnest and lacking proper amounts of snark, but Wednesday’s show was a strangely moving one, most especially at the finish, when Morissette sang “Thank U,” the lead single from “Pill’s” often overlooked followup album, “Supposed Former Infatuation Junkie,” as tweets from fans saying what they were thankful for flashed on the rear screen. There were a lot of cats but also a lot of cancer and COVID diagnoses, and by the time she got to “How about unabashedly bawling your eyes out,” it seemed like a good instruction, even if an impending curfew left time only for a slight welling. The thankfulness didn’t just stop with India, providence and clarity, but for massive pipes, warm nights and survivors’ joy.