The Predators, playing their first game at home, have won three in a row. Winnipeg has dropped two straight.
Jordin Tootoo also scored for Nashville.
The Jets jumped ahead 2-0 in the first period against Chet Pickard, who made seven saves.
Machacek scored on a wrist shot from close range at 5:48. Postma added a power-play goal at 10:27.
Nashville scored four goals in the second period, three on the power play, against goalie Chris Mason.
Tootoo scored Nashville's first goal at 4:50 of the second, and Kostitsyn, Erat and Hornqvist followed with man-advantage goals in a span of 4:36.
Pekka Rinne started the second in goal for Nashville and stopped seven of eight shots. Pickard returned with 5:36 left to play in the period.
Meech scored Winnipeg's only second-period goal, a power-play tally at 6:54.