Some of the anti-depressant meds affect things like GABA or norepinephrine (so an SNRI as opposed to SSRI), so it's not just the anti-depressant angle, as they're often used in much smaller doses than when used for depression.

It's pretty fascinating stuff - I just learned about the norepinephrine angle recently. The thinking is that chronic pain causes people to become more sensitive to small pain signals - their nervous system is over-sensitized to pain, and these meds help with reducing the signaling/response to signals.

If you're curious, lookup gabapentin (it's been around for at least 30 years) or tramadol (an SNRI), which has also been around a long time.