Delaney was 11-for-11 on free throws as the Hokies held off a late charge by Navy in the opening game of the BB&T Classic.
Navy (7-2) held a 34-28 halftime lead, but Virginia Tech (5-3) opened the second half with an 18-2 run and did not trail again.
Vassallo finished with 17 points, and Jeff Allen also had 17 for the Hokies.
Navy's Kaleo Kina had his first double-double of the season with 18 points and 10 rebounds, and Adam Teague added 18 points for the Midshipmen.
Virginia Tech outrebounded Navy 45-28, with Vassallo and Cheick Diakite each picking up eight.