been following the rivalry since the 60's
when VT won 6 games UVA won 1
70's VT won 4 UVA won 4 one tie
80's VT won 6 UVA won 4
90's VT won 5 UVA won 5
2000-2010 VT won 9 UVA won 1
2011-2106 VT won 6 UVA won 0

so over the last 6 decades UVA has never had more victories over VT and has tied them on A decade basis 2 times in the 70's and the 90's.
That's a total of 36 wins for VT 15 for UVA and one tie
UVA's win percentage over the last 6 decades has been 28.8% VT's win percentage has been 69%
So to your question, the dominance started in the mid 90's right after the sanctions came off from the Dooley era (its a shame Dooley/VT didn't have the fortune his UNC brethren have now)
Cornell Brown is the player Beamer credits for the turn around of the program but in all honesty, the numbers would show UVA achieved the most when VT was on sanctions