Jennifer Aniston & Justin Theroux -- Surprise, We're Married!!! (PHOTOS)

Jennifer Aniston and Justin Theroux had a surprise wedding at their Bel Air mansion last night -- telling all their celeb pals it was just a birthday party, but then did the deed, instead.

Our sources say Jen told friends she was throwing a surprise 44th bday bash for Justin. Great cover, and friends like Howard Stern, Chelsea Handler, Sia, Lisa Kudrow and John Krasinski showed up -- but TMZ knew something was up Wednesday afternoon when we spotted a very wedding-ish cake going into the house.

It had TWO muppet-like characters -- male and female -- on the top. If it was just a birthday party for Justin ... why have 2 people on the cake?

Second major clue -- an actual man of the cloth! A pastor WITH bible in hand was walking into the house.

We're told a giant shed was built over the past week to hide all the furniture and party supplies -- which were set up in the backyard yesterday afternoon. Jen went to great lengths to keep everything under wraps -- we're told staffers' phones were confiscated all week, and no parking was allowed near the property.

Mazel tov!