The popularization of the analogy appears to be from Philip Siekevitz, a cell biologist; from an article "Powerhouse of the Cell" in Scientific American in 1957 (https://www.nature.com/scientificamerican/journal/v197/n1/pdf/scientificamerican0757-131.pdf).

That being said, while he may have popularized it, it's clear from his paper that the "powerhouse" and engine analogies predate him. It it appears that as early as the 1920s, the mechanism of cellular respiration (not yet definitely located to the mitochondrion) were being described in terms of engines. The discovery of the Krebs cycle in the 30s, which was localized to the mitochondrion, was also described in as being similar to a power plant.

I'm using a secondary source here (I can't read German, plus most of this is WAY over my head anyway) but it appears that once cellular respiration was localized to the mitochondrion, the "power plant" analogy seemed apt -- so much so, that by 1957, it was the natural analogy to make for a general audience for Siekevitz.

Source: Ernster L and Schatz G, Mitochondria: a historical review, J Cell Biol. 1981 Dec;91(3 Pt 2):227s-255s. (free on PMC https://www.ncbi.nlm.nih.gov/pubmed/7033239)