News spreads fast in the Big Easy ... 'cause Taylor Swift and Travis Kelce grabbed dinner together Friday night -- and their way in was devoid of commotion ... but their exit was insane!

The super-high profile couple was spotted walking into a New Orleans uptown restaurant ... where a few people were clearly tipped off they would be there ... and they made sure to tell TS how much they loved her.

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Sure hope that meal was relaxing ... 'cause the duo's exit was anything but ... as word clearly got out they were there -- and a huge hoard showed up, screaming and snapping pics as they left.

The date is a big deal for a few reasons ... the biggest being, this is the first time TS has been spotted since TMZ broke the news that her relationship with Blake Lively is pretty much toast after TS was dragged into the Justin Baldoni war.

Of course ... it was also the first time Taylor and Travis had been spotted together in NOLA, where TK and his Chiefs hope to make history with a Super Bowl three-peat on Sunday.

We know TS will be at the big game, cheering him on as loud as she can ... and we definitely know Blake will not be included this time around.