Graeme Jones' men were up against it from as early as the fourth minute when Marley Watkins bundled home from close range.
City were worthy winners against a disappointing Hatters side, with Lee Johnson's men even having the luxury of being able to miss a first-half penalty.
The loss saw Luton drop to second bottom in the Sky Bet Championship, with Barnsley edging above them thanks to a 0-0 draw at Swansea City.
Here's how the Luton players rated in the Ashton Gate reverse.
13. Alan Sheehan 5
Replaced LuaLua late on. It was good to get him some game time because, as a defender with experience, and as a leader, he could provide a bit more solidity at left back in the coming games | freelance Photo: Liam Smith
4 / 4