Edmunds finished with 74 yards on 14 carries. Logan completed 25-of-31 passes for 366 yards.
With the victory, the Hokies (7-3, 4-2 ACC) pulled into into a virtual tie atop the ACC's Coastal Division with Miami (7-2, 3-2) and idle Georgia Tech (5-2).
Joshua Stanford compiled 107 yards with a TD on seven receptions for Virginia Tech.
The Hurricanes, meanwhile, dropped a second straight despite 324 yards and two touchdowns from Stephen Morris, who made good on 16-of-29 passes.
Dallas Crawford, subbing for injured star running back Duke Johnson, managed just 37 yards and a touchdown on 10 carries.