Glen Powell and Michelle Randolph Vacation Together in Miami

Glen Powell and Michelle Randolph are officially turning up the heat ... the new couple was spotted sneaking in a South Florida getaway over the weekend.

TMZ obtained photos of the pair leaving 1 Hotel South Beach in Miami on Saturday and making a beeline for a private airport. The duo didn't go straight there, though. They made stops for gas and even swung by a smoke shop along the way. Glen showed he's still got his leading man manners, holding the door open for his new girlfriend like a total gentleman.

Sources tell TMZ ... the romance is moving fast, and after leaving Miami, the couple took things international, jetting off to the Caribbean hot spot of St. Barts to keep their holiday vacation going.

The night before they jetted out of South Florida, Glen and Michelle were photographed returning to the same hotel after grabbing dinner with friends at celebrity favorite Papi Steak.

The two sparked romance rumors back in the fall after being spotted dancing together in Glen's hometown of Austin, Texas. Since then, they've been inseparable ... popping up together at his "Saturday Night Live" hosting gig and even an F1 party in Miami.