EXCLUSIVE

Eliza Dushku was robbed blind Saturday morning in Rhode Island by 2 guys in costume ... and the scary part -- she had to sleep in the same hotel as them afterward.

Providence police officials tell us Dushku was unloading items from her vehicle around 3:45 A.M. ... when she set her Louis Vuitton bag on the curb and the jerk thieves snatched it up.

One was dressed as Caesar, the other was wearing a random mask.

Cops say they scoured security footage and saw the purse snatchers get into an elevator ... but they couldn't tell where they got off.

Dushku tweeted saying, "Really upset. It's been a long night. The 2 men are in my hotel currently & 'nothing can be done."'

She added, "If you see anyone walk out of hotel w this Duffel bag, it was a gift from @MrsSOsbourne ON her show in '04. It's been around the world w me."

Cops are on the hunt ... but it's tough.

7:15 AM PST -- Eliza tweeted saying the men were caught by police officers this morning in the hotel ... and they still had the luggage on them. Dushku claims they were promptly arrested.