The lines that divide tribute from parody or pastiche are very fine ones, and the concepts are hardly mutually exclusive — especially in the music world. Songs ranging from Billy Joel’s “Uptown Girl,” Madonna’s “True Blue” and Whitesnake’s “Still of the Night” to Bruno Mars and Anderson .Paak’s recent hit “Leave the Door Open” — not to mention many titles in Beck’s catalog — are like giant musical winks, knowing grins directed at target audiences who not only get the references but are also in on the joke. None of which is to say the above songs aren’t good or even great: The jokes are inclusive because the artist knows most of their listeners will pick up on them, but also not so specific that they alienate people who don’t.

One could argue that Michigan quartet Greta Van Fleet’s entire existence is based in this kind of homage/parody, especially when one considers that the three-fourths-sibling group, all of whom are in their early or mid-20s, plays a style of Zeppelin-esque, blues-based hard rock that is two or even three times older than they are. Brothers Josh, Jake and Sam Kiszka (on vocals, guitar and bass, respectively), along with unrelated drummer Danny Wagner, do it exceptionally well, although the clichés in their music are so big, bold and intentional — particularly Josh’s at-times comically skyscraping falsetto — that it’s almost impossible not to laugh. The group lit up rock radio — hell, they could have been genetically engineered for rock radio — and indisputably established themselves with their Grammy-winning 2018 debut album, “Anthem of the Peaceful Army,” but set their sound so firmly in stone that it would seem to have left them little room to progress.

Happily, that notion underestimates both the band and, not least, its record label, Lava Records, which was founded by veteran A&R executive Jason Flom, who cut his teeth on hard-rock acts of the ’80s but also signed Tori Amos, Katy Perry and Lorde. That expertise and versatility comes into play on “The Battle at Garden’s Gate,” which sees the group teamed with two-time Grammy-winning producer of the year Greg Kurstin, who has worked with Adele, Sia, Kelly Clarkson and Paul McCartney — and also Beck and the Foo Fighters. Needless to say, he gets Greta Van Fleet, and helps them to define the path forward.

That path, essentially, is doubling down on the influences. Without drawing too fine a parallel, much of “Battle” evokes mid-’70s Rush — circa “2112” and “A Farewell to Kings” — with a nod to the Zeppelin albums that influenced those works. It advances the formula of the group’s earlier, more basic recordings with lots more keyboards and acoustic guitars (and even strings) and slower songs, many with quasi-philosophical titles like “Age of Machine” and “Built by Nations.” Several of those tracks are epic in their ambitions: More than half hit the five-minute mark, and one is almost nine minutes long — all of which, of course, only makes the album truer to its forebears (speaking of which, the coda of “Broken Bells” evokes Donovan’s 1969 anthem “Atlantis”).

But then again, “The Battle at Garden’s Gate” wouldn’t be authentic if it skimped on length or didn’t end with the nearly nine-minute song. The brooding “Weight of Dreams” is heavy on arpeggiated chords and bears more than a trace of Zeppelin’s epic 1976 track “Achilles Last Stand.” It has not one but two false endings: one that turns into a majestic, sweeping coda — complete with a blazing guitar solo, swooning strings and wailing, wordless vocal ad-libs — and a second that’s a moody outro played on acoustic guitar (another genre specialty).

It all gets very “Spinal Tap” at times, but Greta Van Fleet is not a parody act or even, like so many of their predecessors, essentially a tribute band that plays originals. As ripe for humor as the shrieking vocals, the Zeppelin riffs and the Dungeons & Dragons vibe can be, this album proves that the group isn’t only aware of those things — it’s beaten the haters to the punchline. “The Battle at Garden’s Gate” achieves the rare feat of being absolutely hilarious and also one of the best straight-up rock albums to come down the pike in many moons — and anyone who thinks it can’t be both just isn’t in on the joke.