Draisaitl made it 3-2 on a 4-on-3 power play at 13:02.
"We had talked about taking time and space away and we competed hard," Oilers coach Dave Tippett said. "I thought both teams played real hard. Our power play came up big for us. You talk about working for your breaks, we had a couple of real good chances in the first and didn't capitalize, and then at the end of the second we got a break on the first power-play goal."
Smith scored at 12:17 of the first period to give Nashville a 1-0 lead. Bonino made it 2-0 at 17:06 of the second period, redirecting a point shot from Dan Hamhuis.
"I thought we deserved better," Predators coach John Hynes said. "I really liked our game, I thought we played well. I thought we played well enough to win. Unfortunately, a couple of bad bounces went in, particularly the first goal, and then we have to find a way to kill that 4-on-3.
"I think there is a lot to build off tonight's game. Unfortunately, we didn't find a way to be able to win it, but I think if we play like we did tonight, more times than not we're going to find a way to win games."