Virginia Tech was held scoreless into the fourth period before putting together 10 points in a span of 72 seconds to tie the contest.
Journell's field goal came on the opening possession of the overtime and the Hokies won it when Nick Borgese missed a 42-yard field goal try for the Scarlet Knights.
The teams combined for 21 punts and the Hokies (7-6) overcame 190 yards in penalties to avoid what could have been their first losing season in two decades.
Light rain fell during halftime and turned into a downpour during the final two periods.
Rutgers scored all its points in the first quarter on a fumble recovery in the end zone by Khaseem Greene on the second play of the game and a field goal of 36 yards by Borgese.
Virginia Tech finally got on the scoreboard on Journell's 25-yard field goal with 12:14 left in regulation. Three plays into the ensuing possession Rutgers quarterback Gary Nova was intercepted and that led to a 21-yard scoring pass from Logan Thomas to Corey Fuller.
The Scarlet Knights, part of a four-way tie for the Big East Conference championship, finished at 9-5. They lost their last two regular-season games to Pittsburgh and Louisville.
Thomas completed only 15-of-39 passes for 192 yards with two interceptions. Nova was 17-of-40 for 130 yards.