The junior guard's plays saved the day for the Tigers, who rallied from a 56-52 deficit after leading by a dozen points earlier in the second half.
Auburn then ran a set play and was able to in-bounds the ball into the frontcourt to uncovered Quantez Robertson to end the game.
Commenting on the final play, UVA coach Dave Leitao said, "There were two options, one for Sylven (Landesberg) to reject the ball screen and see how far he could take it. Then Sammy (Zeglinski), if his feet were set and it was a quality shot then he could shoot from two or three, if not drive it in and kick it.
"He sprinted off and took the shot and I think it was a little bit untimely because there was a man there. There wasn't that much time left either so maybe he felt like he had to take it."
Jeff Lebo's Tigers improved to 6-4 with the victory while UVA fell to 4-4.
Korvotney Barber came through with a double-double for the short-handed Tigers, who played without guard Frankie Sullivan, who was attending a funeral, and center Brendon Knox, who is ill. Barber scored 13 points and pulled in 14 rebounds.
The Tigers also got double figures rebound totals from Quantez Robertson and Lucas Hargrove, who had 10 apiece. Both Robertson and Hargrove tied their career highs for boards as the Tigers out-rebounded the Cavaliers 44-30.
"We knew Virginia was going to make their run in the second half, which they did, and I thought we made made just key, big plays coming down the stretch and pulled out a W," Lebo said.
Virginia made 18-49 field goals (36.4 percent) and Lebo said defense and rebounding were keys to the victory. "I thought our quickness bothered them," he stated. "We pressured them pretty well and they didn't hurt us inside at all. We did double when it went in there.
"We did a great job in the first half on (Sylven) Landesberg," Lebo said. "I think we had Tez (Robertson) on him a lot in the first half. In the second half they started to post him a little bit and he hurt us in the second, especially getting to the foul line.
"I thought DeWayne Reed did a great job on Zeglinski. He was the key in the game. As he plays well, I think Virginia plays and he didn't score in the first half and Reed made a crucial block on his three-point attempt at the end of the game."
Landesberg, who averages 19.1 points per game, led all scorers with 22 points as he hit 10-14 free throws and 5-8 field goals. Zeglinski scored nine points as he made 4-14 field goals.
The Tigers won the game despite making only 34.5 percent from the field, but the Tigers got off 64 shots compared to 49 for UVA. "It's amazing we won the game shooting as poorly as we did," Lebo said. "Tay Waller missed, I think, eight threes. Six of them were right there, back-rim shots, but he made a crucial one in the last two minutes and so did DeWayne Reed."
The Tigers jumped out to a 9-2 lead, but Virginia caught the Tigers midway through the first half. However, Auburn made a run before halftime to build a 32-21 lead going into intermission.
The score was tied at 21-21 with 6:02 left in the half, but the Cavaliers didn't score again until the second period.
Fastbreak stuffs by Robertson on a pass from Barber and by Rasheem Barrett on a pass from Reed helped the Tigers build a double figures lead as did a slam dunk rebound by Hargrove in the closing seconds of the period.
At the half, the Tigers led due to better shooting and rebounding. Auburn hit 41.9 percent of its shots vs. 20.2 for the Cavaliers and the Tigers held a 21-13 rebounding advantage.
Auburn led 43-32 before the home team made a run to tie the game at 50-50 with 6:29 left on a three-pointer by Sammy Zeglinski. UVA shot 52 percent from the field in the second half.
The Cavaliers led 56-52 when Waller cut the lead to one on a three-pointer with 2:16 to play.
Auburn's defense and the three-pointer by Reed at the 1:38 mark proved to be the difference for the Tigers in taking the road win over an ACC team.
Auburn struggled at the foul line making 8-15 while UVA hit 16-21. Each time had a dozen turnovers.
The Tigers return to action on Monday with a 7 p.m. home game vs. Alabama State.