Vokoun, who allowed 13 goals in Nashville's opening two losses, has starkly turned his early season around. He has been in the nets for each of the Predators three straight victories and stopped 91 of 93 shots.
The Rangers outshot the Predators in every period but lost for the fourth time in five games.
Nichol gave Nashville a 2-0 lead midway through the second period and then helped set up Jerred Smithson's first of the season, a power-play goal with 1:48 left in the frame. Jason Arnott scored his second goal in the first period for the Predators, who have won the first two legs of a three-game swing through the New York metropolitan area.
Nashville edged the Islanders 2-1 in a shootout on Monday and will face the New Jersey Devils on Thursday.
Although they yielded only one power-play goal, the Rangers again took a slew of penalties. Nashville had seven man-advantage situations, including a 5-on-3 and two power plays that started in the final minute of one period and carried over.
New York coach Tom Renney was incensed Monday when the Devils had a 7-1 power-play advantage in the Rangers' 4-2 victory. The Rangers killed them all off, but didn't find the same success in the matchup with the Predators.
The Predators' lead grew to 3-0 when Smithson scored for the first time in 21 games, dating to March 14 of last season.
Earlier in the period, Nichol banked the puck off the right-wing boards and retrieved it after getting around defenceman Marek Malik. Nichol skated out from the corner and cut in front before sliding a shot past defenceman Michal Rozsival and into the lower left corner of the net at 9:42.
Vokoun was sharp throughout and was a key component in killing off all eight Rangers power plays that featured three two-man advantages. The final one came in the final six minutes, and lasted 1:03.
New York tried to find space around Vokoun from long distance, as Jaromir Jagr fired away from the high slot during a second period power play, and from in close, too.
Petr Prucha was denied on three whacks from the left post in the second period, and Matt Cullen was frustrated, too, in the third when Vokoun kept a short flip shot out. Brendan Shanahan rushed in to jab at the rebound, but the goalie covered up.
Henrik Lundqvist finished with 24 saves for the Rangers, who fell to 2-3 at home.
Notes: Shanahan scored on the Rangers' only power-play chance against the Devils on Monday. ... Nashville entered with the worst penalty-killing unit in the NHL (eight goals in 21 chances), but was perfect for the second straight game. The Predators were 3-for-3 against the Islanders and 0-for-2 on their own power play.