The ninth-ranked Nevezis came close to registering the biggest upset of the season in the Betsafe LKL, forcing Zalgiris to work extra hard for an 82-79 victory on Sunday.
Brandon Davies and Aaron White put the Sarunas Jasikevicius-coached hosts ahead in the clutch, while Edgaras Ulanovas capped off the 10-5 run with a pair of free-throws to avert what would have been a highly disappointing outcome.
Nevezis did have multiple attempts to force overtime at the end of regulation, but Adonte Parker and Martynas Varnas couldn't connect on their heavily-contested three-point attempts.
Aaron White was the top scorer for Zalgiris with 16 points, while Artruras Milaknis and team captain Paulius Jankunas chipped in with 12 points apiece in the close escape.
Chauncey Collins finished the contest with a game-high 29 points on 9-of-15 shooting, Adonte Parker scored 22 points, as Martin Junakovic had 10 points.
In the other game of the day, Juventus got back to winning ways with a 96-67 triumph over the bottom-of-the-table Siauliai behind a 16-point and 10-rebound double-double from Martinas Geben.
Vaidas Cepukaitis and Kenny Gaines scored 12 points each, while Dovis Bickauskis and Karolis Guscikas chipped in with 11 points apiece.
For Siauliai, Saah Nimley led all scorers with 20 points, while Cedrick Bowen had 14 points.