Serena Williams is teaching her fetus fiscal responsibility -- going on a late-night Dollar Tree run in Florida ... and TMZ Sports has the pics!

The tennis superstar strolled into the discount shop in Palm Beach around 9 PM in a maxi dress that showed off her growing baby bump -- and bought a bunch of inexpensive stuff!

We're told shoppers quickly recognized Serena and she was super cool -- and even stopped to pose for a couple pics.

And get this, we're told the multi-millionaire -- who's engaged to a super rich tech giant -- is a regular at the shop.

#HowTheRichStayRich