Minutes later, the 75 passengers and crew had perished, and the engine and all six carriages lay at the bottom of the estuary as a result of what remains the greatest structural failure in British engineering history - the collapse of a section of the bridge more than half a mile long.
The Tay Bridge had opened amid great fanfare just 19 months previously. Queen Victoria had made the crossing, afterwards conferring a knighthood on its designer, Thomas Bouch.
But for all their achievements, engineers such as Bouch still had a lot to learn about the forces that nature could bring to bear on their structures. And in the Firth of Tay, the least understood of those forces was the wind.
On that fateful night, gales of up to 70mph were pounding the bridge sideways-on, and a subsequent inquiry found that Bouch's safety margins were woefully inadequate.
While nobody knows for sure what happened, it seems likely that the wind lifted one of the iron supports clean off its base in mid-estuary, causing the structure to overbalance just as the 114-ton train ran on to it. Without modern wind-tunnel tests or computer modelling, Victorian engineers had to rely on their own experience in such matters. Bouch could not easily have predicted how his bridge would behave in a gale, but his reputation was sunk all the same.
The inquiry decided that the project had been rushed. Shoddy workmanship and maintenance had contributed to the collapse, and as Bouch was responsible for both, he shouldered all the blame.
A broken man, he became ill, dying within a year of the disaster at the age of 58.
But while the collapse finished Bouch, it was the making of another man, the self-styled "tragedian" William McGonagall. His clumsy, cloying poem, "The Tay Bridge Disaster", brought him universal fame, helping keep alive the memory of Britain's worst engineering blunder.