The Hokies' eight-match unbeaten streak is the second-longest such streak in school history, trailing only a 9-0-1 stretch in 2005, which stands as the school record.
This was the first-ever draw in 26 meetings between the schools, while the Hokies are 2-1-1 in their last four matches against the Cavaliers. Tech moved to 1-0-2 in three overtime matches this season and is now 4-0-1 when scoring first.
Tech (6-1-2, 1-0-1 ACC) took control of the action in the later stages of the first half with Hock and junior forward Robert Edmans attempting three shots apiece.
Hock had three quality scoring chances within the last 20 minutes of the first half and capitalized on his third and final opportunity in the 34th minute. Edmans got his foot on a cross for a one-time cross at the top right of the box that found Hock in stride 10 yards from the net for his team-high fourth goal of the season with 11:18 remaining in the opening half.
Tech's junior goalkeeper Markus Aigner made his second consecutive start and played all 110 minutes in net. Aigner made a career-high five saves and is now 1-0-2 in three decisions this season.
Virginia (6-1-2, 0-0-2 ACC) controlled the tempo early in the second half and out shot Tech, 13-4. The Cavaliers evened the match at one goal apiece when Yannick Reyering drew a foul in the box and scored his seventh goal of the season with a penalty kick in the 70th minute.
The Hokies made a late surge in the second overtime and Alexander Baden drew a foul in the box for a penalty kick but could not convert the opportunity for the go-ahead goal.
A school record 7,906 spectators filed into Virginia's Klockner Stadium, breaking the previous mark of 7,807 set back in December 4, 1994.
The Hokies play their second consecutive top-five foe by hosting No. 1 Wake Forest at 7 p.m. on Friday in Tech Soccer Stadium.