The newlyweds snuggle in the back of a classic convertible Mercedes as they exit their reception

Credit: Karl Larsen/INF; Inset: Pacific Coast News

They’re on the road to wedded bliss!

Drew Barrymore and Will Kopelman made a romantic exit from their wedding Saturday, snuggling in the back of an old classic convertible Mercedes (with the top up) that was decorated with blush and hot-pink roses as well as pink ribbons.

The newlyweds left the reception, held at the actress’s Montecito, Calif., home, at about 1:30 a.m., and spent their first night as husband and wife at a hotel.

“Drew and Will sat in the back of the car,” a source tells PEOPLE. “They would not stop kissing and looked very cute. Drew was beaming and looked extremely happy. She was still in her wedding dress.”

Barrymore, 37, is expecting her first child with Kopelman, an art dealer.

For the exclusive photos from Drew & Will’s wedding day, pick up next week’s issue of PEOPLE