Watson had two goals and two assists, Calle Jarnkrok scored two shorthanded goals, and Pekka Rinne made 21 saves for Nashville (8-3-2), which had won four straight.
"When you lose a game like this, you want to get back on the ice and get out there as quick as you can," Predators coach Peter Laviolette said. "We've been pretty consistent for the whole year. I think the one thing that we'll go back and look at is that we just really stopped playing the game offensively."
Andersson scored for the Flames to make it 4-2 at 1:58 of third period, and Lindholm scored his 100th NHL goal to cut it 4-3 at 13:38 when his centering pass went in off the skate of Predators defenseman Roman Josi.
"I thought we had the puck lots, and if we didn't, it was the most we had it in a game," Calgary coach Bill Peters said. "I thought we were dangerous, and we were looking to make plays and we were playing with confidence. You can't play with one foot on the gas and one on the brake. So let's take the one off the brake."
Alan Quine scored his first of the season to tie it 4-4 at 16:39 of the third off a cross-ice pass from Mark Giordano.
Nick Bonino gave the Predators a 1-0 lead at 5:33 of the first period on a rebound in front. It was his fourth goal in the past two games.