Blair Walsh kicked five field goals from 22 to 47 yards while the Vikings were building a 22-14 advantage through the early stages of the final period.
Cole then intercepted a pass by Tyler Thigpen and scored with 3:28 to play. On Buffalo's first play after the kickoff, Cole intercepted Brad Smith's throw and brought it back for a score as well.
Minnesota's Christian Ponder completed 10-of-13 passes for 136 yards and a touchdown. The scoring pass was a 1-yarder to Jerome Felton that came at the end of an 80-yard drive in the first quarter.
The Vikings improved to 1-1 in the exhibition campaign. Buffalo is winless in two games.