Ryan Suter and Nick Spaling also scored for the Predators.
Bryan Bickell and Marian Hossa scored for Chicago.
Ellis' goal was a one-timer from high above the right circle at 14:18 of the third period.
Hossa tied it at 2-2 with a wrist shot from above the right circle at 6:05 of the third. It was his 21st goal of the season.
Suter opened the scoring against Chicago goaltender Ray Emery with a shot from high in the slot near the left circle that went into the right side of the net at 18:20 of the first period. Emery had 16 saves.
Bickell tied the game 46 seconds later. His wrist shot from high in the slot beat Predators goaltender Pekka Rinne to his stick side. Rinne finished with 30 saves.
Spaling put the Predators back in front 2-1 at 17:21 of the second period. Ellis sent a shot from the point that deflected high off Spaling's stick and into the net.
NOTES: Patric Hornqvist did not play for Nashville because of an upper body injury. ... Suter has nine points (two goals, seven assists) in his past nine games. ... This was the seventh of nine consecutive road games for the Blackhawks.