I can only narrow it down to two episodes that you could be thinking of: It's either "A Penny for Your Thoughts" or "You Drive," depending on whether the job or the car is the more important factor.

Both episodes are united by the mousiness of the protagonist, a characterization "The Twilight Zone" frequently liked to play with (as you point out, it was also the main feature of the titular "Mr. Bevis" in that famous episode from the show's first season).

In "A Penny for Your Thoughts," a shy bank clerk named Hector Poole (played by comedy star Dick York) gets the ability to read minds after a coin he tosses lands amazingly on its edge. He is nearly hit by a car early in the episode, but otherwise the car is not a big factor in the plot.

"You Drive" is about a nervous man who runs over a paperboy (he's driving a Ford Fairlane, though, not a LaSalle) and flees the scene to avoid the repercussions. He's safe until the car itself seems to come alive and seek vengeance. The man holds a nondescript office job, but it's not central to the story.

As an aside, "You Drive" is also notable for being one of a handful of "Twilight Zone" episodes written by TV great Earl Hamner Jr., creator of "The Waltons" and "Falcon Crest."

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