Brendan Dunlop added 15 points, including two key baskets in the second half that helped turn away Fordham rallies, as the Hokies (13-14) advanced to play East-division top seed Temple on Thursday.
Bevon Robin had 21 points and a career-high 11 rebounds for Fordham (12-15) but the Rams could not recover from a first half in which they shot 8-of-29 from the field (28 percent).
Trailing 51-36 midway through the second half, Fordham used an 8-1 run capped by a Jason Harris 3-pointer to cut the deficit to 52-44 with 8:31 to go.
Roberts responded with a 3-point play after being fouled on a turnaround jumper and Dunlop added two layups in a span of 1:17 as Virginia Tech extended to a 13-point lead and was not seriously threatened again.
Alejandro Olivares added 12 points, 10 in the second half for Fordham, which lost to the Hokies for the seventh straight time. Virginia Tech won its second A-10 tournament game since joining the conference in 1995.
The teams were tied 15-15 with 8:46 left when Virginia Tech pulled away with a 16-4 run. Fordham went cold from the field, hitting 2-of-13 from the field the last 12 minutes of the half.
A technical foul whistled on Fordham's Greg Griffin rattled the Rams further, as the Hokies went on an 8-0 run highlighted by Jermaine Kimbrough's 3-pointer.
Roberts added a one-handed dunk off an offensive rebound late in the half as Virginia Tech took a 33-24 halftime lead.
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