Farrell poured in 22 points for the 10th-seeded Fighting Irish.
Notre Dame was desperately seeking to enhance its resume for NCAA Tournament consideration with the return of senior forward Bonzie Colson, who missed about two months before rejoining the lineup last week.
Notre Dame (20-13) meets fifth-ranked Duke, which is the tournament's second seed, in Thursday night's quarterfinal round. This will be a rematch of the 2017 conference title game, which was won by Duke.
The Fighting Irish had a tussle to defeat last-place Pittsburgh on Tuesday and they started slow the next night.
Rex Pflueger scored 14 points, TJ Gibbs added 13 points and Colson provided 12 points for Notre Dame in the Virginia Tech game.
Farrell drained four 3-point baskets as part of the team's 10-for-29 long-range shooting.
A 14-0 run turned a 59-52 deficit into a 66-59 lead for the Fighting Irish.
That was after Virginia Tech's 21-point lead was reduced to 54-50 with 7:45 to play.
Justin Bibbs and Justin Robinson each scored 15 points for Virginia Tech (21-11). Chris Clarke supplied 12 points.
Colson made a banked-in 3-point basket for a 60-59 lead with two minutes to play to provide Notre Dame with its first lead since the opening minutes.
Colson added two free throws at the 1:14 mark and Farrell had two more free throws for a five-point lead.
Notre Dame had a stretch bridging the two halves when it scored on only 3 of 25 possessions.
Virginia Tech led 47-26 after Kerry Blackshear Jr.'s bucket at the 15:07 mark. Another minute elapsed before the Fighting Irish got untracked to begin their comeback.
The seventh-seeded Hokies held a 34-21 halftime lead, using a 16-2 run to take a 10-point lead before extending that.
Notre Dame shot 8-for-32 from the field in the first half. Colson started out 1-for-9.
--Field Level Media
Notre Dame | Virginia Tech | |
Matt Farrell 22 | Scoring | Justin Bibbs 15 |
Temple Gibbs 7 | Assists | Justin Robinson 7 |
Rex Pflueger 9 | Rebounds | Kerry Blackshear Jr. 8 |
Matt Farrell 8 | Free Throws Made | Justin Robinson 5 |
Rex Pflueger 2 | Steals | Justin Robinson 3 |
Bonzie Colson 2 | Blocks | Nickeil Alexander-Walker 1 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Notre Dame | 71 | 37.7 | 10-29 | 21-25 | 13 | 37 | 2 | 3 | 11 |
Virginia Tech | 65 | 41.7 | 8-30 | 7-9 | 15 | 30 | 1 | 6 | 10 |