Taylor Swift and Travis Kelce rang in his 37th birthday Monday night at a dinner date in the Big Apple ... their first birthday celebration as a married couple.

Taylor and Travis hopped out of a black SUV in Manhattan's Soho district and were greeted by a swarm of paps on their way into Torrisi ... an Italian joint.

Travis was in double celebration mode ... not only was it his birthday, but it was also "Victory Monday" ... his Kansas City Chiefs were fresh off a victory Sunday over the Las Vegas Raiders.

The couple picked a fancy restaurant, which is no surprise ... a quick glance at the menu shows a bunch of pricey dishes ... such as the $42 Raviolini with Blue Prawns and Saffron, the $44 Linguini and 15 Pink Littleneck Clams, the $59 Duck Alla Mulberry and the $72 Dover Soul Francese.

Don't worry, they can afford it.

Taylor and Travis looked terrific in their get-ups last night. Taylor sported a black dress topped off by a leather jacket. Travis opted for a green cardigan sweater, charcoal slacks, and black dress shoes.

Talk about great timing ... the Chiefs have their bye week, so Travis has some extra time to spend with Taylor ... his NFL team doesn't play again until Oct. 18.

Happy birthday, Travis!!!