Capitals forward Alex Ovechkin had his four-game goal streak end (seven goals).
Tommy Novak gave the Predators a 1-0 lead at 4:10 of the first period when he took advantage of a turnover along the boards, skated to the edge of the right face-off circle and beat Lindgren with a wrist shot.
Milano tied it 1-1 at 9:52, knocking in the loose puck after Conor Sheary's shot hit the right post six seconds after a Washington power play ended for his 100th NHL point.
"It's just my spot on the power play is up front," Milano said. "So, that's where I hang out, and I think [Sheary's shot] hit off a post and I just tapped it in."
Trenin batted in a bouncing puck in front of the net to put the Predators ahead 2-1 at 15:09.
Aube-Kubel tied it 2-2 with an individual effort at 11:07 of the second period. He entered the zone on the rush, faked a shot, skated around Predators forward Nino Niederreiter and beat Lankinen between the pads for his second goal in as many games.
"Yeah, maybe because it was a forward playing there in the middle, so by faking the shot maybe he didn't see it coming," Aube-Kubel said. "Took advantage of it, I guess."