Final answer:
The gaslight is the invention that transformed stage lighting into a more controlled aspect of drama, with the electric light, notably the incandescent bulb invented by Edison, further revolutionizing the field.
Step-by-step explanation:
The invention that brought lighting to the stage in its modern form and made lighting a more controlled part of the drama is C) the gaslight. One of the more recent additions to theatre production is lighting design, which began to reach its full potential with the advent of electric light in the late 19th Century, after the introduction of the incandescent light bulb by both Joseph Swan and Thomas Edison.
It was Edison's practical incandescent light bulb, patented in 1879, that greatly enhanced the capability for stage lighting by providing a reliable, safe, and controllable light source.