How did "kill" get its positive connotations?

For example:

• She made a killing on the stock market.
• The comedian killed the audience — they were slain with laughter.

Did this meaning develop slowly over time or did some person or institution invert the definition?

Etymonline has an entry for killing:

mid-15c., prp. adjective from kill (v.). Meaning "very funny" is from 1844. As a noun, "large profit," 1886, American English slang.

While its usage to mean "very funny" is partly covered in another question, its usage via idioms like to make a killing to indicate a "large profit" dates back to 1886 (as noted above). The American Heritage Dictionary of Idioms has the following to say about make a killing:

make a killing Enjoy a large and quick profit, as in They made a killing in real estate. This expression alludes to a hunter's success. [Slang; late 1800s]

The Online Etymology dictionary states:

killing (adj.) mid-15c., prp. adjective from kill (v.). Meaning "very funny" is from 1844. As a noun, "large profit," 1886, American English slang.

Since the basic meaning of killing is "an act of causing death" I don't think either are surprising slang derivations.

You can either "kill people with laughter" (stop it, you're killing me!) or vanquish your foes in the financial realm (I'm making a killing in the stock market.)