Robert Godhigh also ran for a touchdown for Georgia Tech (5-3, 4-2 Atlantic Coast Conference), which never trailed and responded every time Virginia (2-6, 0-4 ACC) made it close.
Sims scored on the Yellow Jackets' third play of the game and sealed it with a 29-yard TD run with 1:55 left after Virginia had cut the lead to 28-25 on David Watford's 12-yard touchdown pass to Darius Jennings and 2-point conversion pass to Khalek Shepherd.
Earlier in the fourth quarter, Virginia had cut Georgia Tech's lead to 21-17 on Watford's 5-yard touchdown pass to Jennings. But the Yellow Jackets responded with a 65-yard touchdown run by Godhigh to again stretch their lead to double digits.
Georgia Tech got lots of big plays from its triple-option offense, rolling up 507 yards as three backs rushed for over 100 -- Laskey with 133, Godhigh with 111 and Sims with 107.
Virginia got no points off Georgia Tech's turnovers -- three fumbles and two Anthony Harris interceptions -- but moved the ball well against the nation's 12th-rated defense. Watford was 43 of 61 for 376 yards for the Cavaliers, whose 444 total yards were over a 100 more than Georgia Tech has allowed on average.
Two veteran Virginia receivers who have yielded playing time recently to younger players found plenty of open space in the Georgia Tech secondary and had career days. Jennings, a junior, had 13 catches for 119 yards and two touchdowns and senior Tim Smith had 10 receptions for 151 yards. It was the first time in Virginia history two players caught at least 10 passes in the same game.
The Cavaliers had the ball nearly 10 minutes longer than Georgia Tech, which entered the game No. 2 in the nation in time of possession.
However, Virginia failed to capitalize on some key opportunities. Perhaps the most glaring missed chance came late in the first half after a Harris interception gave Virginia the ball at its own 41. The Cavaliers quickly moved to the Georgia Tech 14 on three passes from Watford to Jennings. A pass interference penalty against Louis Young in the end zone put the Cavaliers at the 2.
Kevin Parks was stopped at the 1 with six seconds left, and Virginia burned its last timeout. Rather than settle for the chip-shot field goal, the Cavaliers ran Parks off tackle again. The Yellow Jackets stopped him short of the goal line and jubilantly sprinted into the locker room with their 14-10 lead intact.
It was the second time a gamble failed to pay off for Virginia. On their second possession of the game, the Cavaliers lined up for a 32-yard field-goal try on fourth-and-6. An offsides penalty against Georgia Tech made it fourth-and-1, and the crowd pleaded with coach Mike London to go for the first down. He obliged, but Watford overthrew fullback Billy Scrobacz in the flat.
The game started with a here-we-go-again feeling for the Cavaliers, who gave up a 70-yard touchdown to Georgia Tech on the first play of last year's loss to the Yellow Jackets, when Sims scored on a 36-yard burst up the middle barely over a minute into the game. The score came after a 35-yard run by Goodhigh.
But the Cavaliers settled in after that, forcing fumbles on Georgia Tech's next two possessions and a punt on the third that pinned the Cavaliers at their 2. Virginia responded with a 13-play, 87-yard drive capped by Alec Vozenilek's 28-yard field goal to make it 7-3.
Georgia Tech stormed back with a 59-yard kickoff return by Lynn Griffin to the Virginia 41. Seven plays later, Laskey scored from the 7 to extend the lead to 14-3.
Virginia went right back to work on offense, driving 73 yards in 10 plays to make it 14-10 on Parks' 6-yard touchdown run.
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Ohio State remained No. 1 in the AP Top 25 and tied a poll record Sunday despite lagging support from voters. Meanwhile, No. 2 TCU and No. 3 Baylor edged forward and No. 4 Michigan State slipped.
Texas cornerback Kris Boyd has apologized for retweeting a Texas A&M fan during halftime of Texas' 50-7 loss to TCU on Saturday.
The Big 12 on Sunday acknowledged an officiating mistake that incorrectly awarded Oklahoma State a first down Saturday and said the officials involved would be disciplined.
Georgia coach Mark Richt says he's sticking with Greyson Lambert, who was just 10-for-24 for 86 yards in a loss to Alabama, as the Bulldogs starting quarterback.
Will Grier threw four touchdown passes to four receivers -- all in the first half -- and No. 25 Florida downed third-ranked Mississippi 38-10 on Saturday night.
Leonard Fournette highlighted his SEC-record third straight 200-yard game with a 75-yard touchdown run, and No. 9 LSU overcame Eastern Michigan 44-22 on Saturday night.