The oldest example I know of is Mark Twain’s “Puddin’head Wilson”, where that newfangled technique called fingerprinting solved the mystery. Any other fictional examples of murderers undone by new technology they hadn’t counted on?
Hek Ramsey and Briscoe County Jr… But those are fairly modern creations simply placed in those earlier times…
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I suppose Genesis 4:10 could be DNA evidence … 
Sherlock Holmes beat Puddin’head by four years in The Sign of The Four published in 1890, although fingerprints aren’t central to the story in the same way. And Holmes used various other forensic techniques - tracing the quirks of a typewritten document back to a specific typewriter, handwriting analysis, footprint analysis.
Call Northside 777 is a film, but it uses lots of “new-fangled” tech. Jimmy Stewart has a small snapshot camera that he takes clandestine photos with. Small camera were new-- they had just recently been the huge ones with the really big flashes, that a child couldn’t lift. This one fit in Stewart’s breast pocket.
The film also uses “zoom and enlarge” technology on a photo-- ad absurdum, but it really was new technology then-- that an enlarged photo wasn’t just a blur. And it used a wire to transmit a photo image. Brand new technology.
There’s also a B-grade Bela Lugosi film called Murder by Television, when TVs existed in labs, and people could read about them in magazines, or see them at exhibits, but they weren’t available commercially yet.
Does it have to be fictional? I read this very good book last year, about the first ever murder solved by the then-newfangled “telegraph” system. But it’s all true.
Depends on your definition of detective, but in a Plastic Man comic, Plas faced a villain who committed crimes by using a super slippery oil, spreading it behind him so anyone pursuing would slip and fall. Plas was able to counteract the oil by using a new chemical.
Detergent.
The newly invented/discovered detergents also played a key role in the solution of a Perry Mason novel. I think it was called “The Case of the Drowning Duck”, but don’t hold me to it, it’s been decades since I read it.
There was a series of rapes in Louisiana back in the late 1990s. When Hawkeyeway wasn’t hosting the Straight Dope chats on AOL with me he had a day time job as a Forensic Biologist (I guess). He was the first to extract DNA from a cigarette butt and it resulted in a Deputy Sheriff being convicted as a serial rapist.
There also was the case of murderer Hawley Crippen who was apprehended after US authorities were contacted by wireless.
It’s not really what to OP is asking, but there is a scene in a 1916 movie called Intolerance (“The Mother and the Law” sequence) where the “new-fangled” automobile, which isn’t as fast as the locomotive, and at first is trying to race it and failing, suddenly starts taking shortcuts. Many are on “horse roads, and one is across a field.” The auto arrives at a location before the train, thereby getting a written pardon from the governor to a gallows ahead of a hanging, saving the [actually innocent, which the audience knows] condemned man. It’s very suspenseful, containing cuts between the train steaming along at a very fast speed, and the car puttering along twist and curves, getting stuck once, but getting unstuck. It’s a 1916 automobile, and not a luxury model. I was on the edge of my seat the first time I saw it. I can only imagine what it was like for audiences in 1916. It must have been like getting to see the end of Alien in the theater in 1979.
Arthur B. Reeve is forgotten today, but he was by far the leading American mystery writer in the first part of the 20th century. He wrote 82 short stories and 26 novels about Craig Kennedy.
He uses his knowledge of chemistry and psychoanalysis to solve cases, and uses exotic (at the time) devices in his work such as lie detectors, gyroscopes, and portable seismographs.
Some of his stories still read as remarkably modern.
Generally speaking, mystery writers have always, from the very beginning, tried to slip in the latest crime detection technology. And also the very latest methods to commit crimes. Right after WWII, for example, a number of mysteries used radioactive materials to commit murders. Anything that got into the newspapers was used pretty immediately in a mystery story.
The Murdoch Mysteries TV series from Canada is all about this. It starts in I think 1896 and Detective Murdoch invents and uses all kinds of technologies. First seasons are great, kind of jumped the shark by season 10 or so.