A source tells Us that the pair first met at Vanity Fair's star-studded Oscars party last month. At the time, Evans, 33, looked dapper in a midnight-blue Gucci tux. Phil Collins' daughter, meanwhile, showed up with a new pixie cut and looked glam in a shimmering black Zuhair Murad Couture gown.
"It's just the beginning stages," a second insider tells Us. "But they're having a lot of fun and seeing where it goes."
Evans previously dated actress Jessica Biel from 2004 to 2006. (The 7th Heaven alum is currently expecting her first child with husband Justin Timberlake.) The Avengers: Age of Ultron star most recently split from Minka Kelly for the second time in October 2013. They first parted ways in 2007 before reconnecting in 2012.
Collins, 25, was last linked to Australian actor Thomas Cocquerel in February 2014. Before that, she dated her Mortal Instruments: City of Bones costar Jamie Campbell Bower, Taylor Lautner, and had a brief romance with Zac Efron.