Sources close to the couple tell TMZ ... Courtney got engaged to Jared Safier last Tuesday at the Beverly Wilshire Hotel -- the one made famous by "Pretty Woman" -- and talk about not wasting any time. The new engagement went down one week after she shockingly flushed a 5-carat rock.

We're told Jared, an Emmy-winning producer, presented her new diamond while they were at the hotel's THE Blvd Restaurant & Bar -- but he saved the traditional down-on-one-knee moment for when they got back to their Brentwood home.

As for the ring deets, our sources say Courtney and Jared were strolling past all the diamonds on display in the hotel's lobby back in February during an Oscars party ... and that's when she spotted the specific ring she liked.

Jared's clearly got a great memory, because we're told he bought the exact ring -- another dazzling 5-carat, radiant-cut VVS rock.

We're told early on in their relationship, which started last summer, they both saw marriage in their future -- so, when the time came, it all felt natural.

As of now, they're not diving into wedding planning, just basking in the glow of their engagement. It's his first time, while she's hoping this third time is her charm.

You'll recall ... Courtney says she was inspired by James Cameron's "Titanic" scene when she casually flushed the engagement ring from her ex-fiancé Chris Sheng a year after they officially split. Boy, that's gotta make Jared nervous about the huge diamond he just bought.