Taylor Swift and Harry Styles leaving the Crosby Hotel
Miles Diggs/Splash News Online
12/07/2012 AT 11:30 AM EST
12/07/2012 AT 09:35 AM EST
Their romance is heating up!
New couple Taylor Swift
and One Direction's Harry Styles stepped out at New York's Crosby Hotel on Thursday night to celebrate a friend's birthday – and get in a little PDA of their own.
Joined by Dianna Agron, Emma Stone
and about a dozen guests, Swift, 22, dressed demurely in black, and Styles, 18, watched as a cake was served and helped to sing along to "Happy Birthday" at the hotel's Crosby Bar.
"Taylor and Harry
[were] being very smoochie," a source at the party told PEOPLE. "They definitely [looked] like a couple."
According to the source, Swift (who is up for three Grammys) and Styles held hands and he seemed "really protective of her" and kept his arm around her during the party.
They shared plenty of kisses, too, and didn't seem to mind if anyone saw. Says the source: "They're not trying to hide it. The bar was packed."
Their outing marks a string of get-togethers in New York City over the past week.
On Sunday they visited the Central Park Zoo together
. And on Monday, Swift attended a Madison Square Garden show afterparty at the Hudson Hotel for Styles' band, One Direction, where the couple joined for a karaoke duet of a Backstreet Boys song. Swift later sang a One Direction tune, before the couple returned to her hotel
around 4 a.m.
Reporting by JENNIFER BRADLEY FRANKLIN