Big mistake, Kate Hudson ... HUGE -- the actress got sucked into a paparazzi vortex all because she unwittingly decided to walk by the NYC hotel where Tom Cruise is staying.
We just posted the video of Tom and Suri Cruise leaving the Greenwich Hotel ... surrounded by eager fans and paps -- but earlier in the day it was all lenses on Kate.
It's pretty clear from the photo ... Kate quickly realized her misstep and did her best to get outta Dodge.
Greenwich Hotel ... busiest sidewalk in the city.