Troy Terry scored twice for the Ducks (23-42-3), who have lost six straight (outscored 31-7). Lukas Dostal made 23 saves.
With the loss, Anaheim was eliminated from Stanley Cup Playoff contention.
"I thought we played a good game," Ducks coach Greg Cronin said. "I mean, we got them in a back-to-back. I thought we had energy and pop.
"Again, you can't win a game giving up three power-play goals, right?"
St. Louis scored three power-play goals in a 7:40 span in the third period.
Thomas put the Blues in front 2-1 at 1:53, scoring with a wrist shot from the top of the right circle with Neighbours in front of the net.
Neighbours then made it 3-1 at 6:12 when he tipped in Brayden Schenn's shot from the left circle.
"I think it's effective. It's tough for a goalie to react when pucks are changing direction right in front of them," Neighbours said. "I'm trying to get better at it and work at it.
"I'm kind of lucky. I was trying to tip it down and it went up. I'll take the lucky bounce. That's 'Schenner' just being a smart shooter. He sees the goalie can't really see the release and just puts it in a good spot. I got a lucky bounce."