The goal was Terry's 18th of the season, second among team leaders, and his fourth point in the last five games. Terry now sits one point shy of clinching his fourth straight 50-point season.
With an assist, Vatrano moved within two of his career high (23) set last season.
Nashville pulled back even in the third period with a power-play goal, a one-timer from the point by Vrana that bounced out of Dostal's glove and over the goal line.
Claimed on waivers by Nashville earlier this month, Vrana's goal was his first as a Pred.
Killorn would restore the Anaheim lead just past the midway mark of the third though, finishing off a well-executed rush sequence in transition. Zegras skated the puck through neutral ice after a Nashville turnover, kicking it wide to Carlsson before getting a pass back in the middle of the ice, and then spinning a setup feed to Killorn right in front of Saros - where the veteran swiped it home around the goaltender's outstretched right leg.