In his 1953 novel, Bring the Jubilee, Ward Moore imagined an alternative history in which General Lee won the battle of Gettysburg and became the president of a Confederate America. It’s a fine story, although, like many books in the genre, the author is forced to spend an uncomfortable amount of narrative time doling out chunks of information to his reader: setting in place what has changed – and, crucially, what has not – as a result of the nudge given to history. It was a problem that beset Laurent Binet more recently in Civilisations, which imagined what would have happened had the Spanish failed in their attempts to conquer South America. That book was wonderful, but Binet kept having to interrupt the rollicking plot to catch up the reader with the onward march of (alternative) history. It feels like it’s a problem that is baked into the genre itself: if you are going to rearrange the furniture of history, it creates a lot of housekeeping.

This is particularly true if, like Spufford, your alternative history diverges significantly from the world as we know it. Spufford’s “what if” is a fascinating one: he imagines that the variant of smallpox that arrived with European settlers was variola minor, both dramatically less fatal than variola major and conferring immunity on those who contracted it. This virological sleight of hand means that, far from being almost entirely wiped out (it’s estimated that between 90-95% of Indigenous peoples in North America were killed by smallpox and other European diseases), there is a huge and thriving Native American population in the US in 1922, when this novel is set.

There’s a risk that this review falls into the same trap as the novel, but to set the scene further, we are in the sprawling and violent city of Cahokia in the state of Deseret, outside the Union but increasingly drawn into domestic US events. Deseret was actually a state proposed by the Mormons in the 19th century, but here it makes up a vast swath of the midwest, sitting above the Navajo state of Dinétah. Cahokia is home to takouma – Native Americans; taklousa – people of African origin; and takata – Europeans. Anopa is the lingua franca of the many tribes that live in Cahokia and the reader slowly picks up a working knowledge of the language.

Spufford is one of our most interesting and unpredictable writers – his career has leapt from memoirs to essays and then, via a kind of fact/fiction mashup (Red Plenty), to two superb novels: Golden Hill and Light Perpetual. Here, he uses his great skill as a storyteller to create a fictional world that, like another alternative history – Philip K Dick’s The Man in the High Castle – has a great deal to say about contemporary America, particularly the issue of race.

The novel opens with a gruesome murder: a lowly worker has been eviscerated, his body left on the roof of the Land Trust (land ownership and utilities are communally owned in Cahokia). Our protagonists are two hard-bitten cops: Phineas Drummond – venal, sly, prone to violence – and Joe Barrow – huge, decent, a pianist and, crucially, Native American, although unable to speak Anopa, having been adopted as a child. The dead man had an Anopa word, Bashli, scrawled on his face in blood. A kind of revolutionary cry of the Indigenous people, it sends the detectives off into the takouma neighbourhoods looking for answers. They meet the leader of the takouma people, known as “The Sun”, and his languorous, beautiful niece, “The Moon”, who point them towards a different interpretation of the murder.

Here the plot ratchets up: we encounter grisly Aztec rituals, a resurgent Ku Klux Klan headed by many of the most prominent takata businessmen of the city, police corruption and shady newspapermen. There’s also a love story. The novel is divided into sections spanning six wintry days, each of them so full of action and information that you have to check to ensure that you haven’t skipped forward in time. How you get on with Cahokia Jazz will depend largely upon how much patience you have for exposition, the extent to which you object to your noirish thriller being interrupted by chunks of expository dialogue. To my mind, Spufford gets away with it: even within the context of a genre that requires the author to carry out so much visible world-building, his flights of imagination and generosity of spirit carry the reader along. Cahokia Jazz joins Robert Harris’s Fatherland and Keith Roberts’s Pavane as a classic of alternative history, further evidence of Spufford’s range and subtlety as a novelist.

• Cahokia Jazz by Francis Spufford is published by Faber (£20). To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply