A strong challenge from Nevezis made Zalgiris sweat with a second-half comeback, but the defending Betsafe LKL champions held on to take a 79-73 victory on the road in Kedainiai.
The top-of-the-table Kaunas club improved to a 22-3 record and kept a one game lead over second-placed Lietuvos Rytas, with Nevezis dropping to 6-19.
Zalgiris started the game with on a 33-8 tear but Nevezis stabilized the situation with a 23-8 run of their own to get the margin to 41-31 at the halfway point in the game.
The hosts were down just 71-69 with under two minutes left, but Zalgiris solved the situation by going on a 6-0 run after baskets from Brandon Davies, Vasilije Micic and Kevin Pangos.
Davies was the top scorer for the winners with 17 points and 9 rebounds, Micic and Paulius Valinskas scored 13 points each, while Arturas Milaknis chipped in with 12 points.
For Nevezis, James Woodard had a game-high 14 points, Justas Tamulis and Aleksandr Zakharov had 11 points each, while Giedrius Staniulis added 10 points and 7 rebounds.