The right-hander, who opened the season at Double-A, didn't have his passport with him when the Twins promoted him from Triple-A Rochester and picked him to start against the Blue Jays in Toronto on Wednesday.
Early Sunday morning, Duffey's father flew from Houston to Rochester with both their passports. From there, father and son made the 170-mile drive across the border to Toronto.
"We took the scenic route," Duffey said. "It's been a pretty wild 48 hours."
The pair crossed at Niagara Falls but didn't stop to check out the view.
"We were both pretty sleep-deprived at that point," Duffey said.
Duffey went 6-8 with a 2.66 ERA in 21 games at Double-A and Triple-A this season. He takes the place of left-hander Tommy Milone, who was put on the 15-day disabled list Sunday with a strained elbow.
Right-hander Ryan Pressley (right lat strain) was transferred to the 60-day disabled list to make room on the 40-man roster.