Jordan Binnington made 24 saves and tied Grant Fuhr for fourth place in Blues history with 108 career wins. Brayden Schenn, Jordan Kyrou and Alexey Toropchenko also scored for St. Louis.
''Pretty good game all around from everybody,'' Blues coach Craig Berube said. ''I thought we got contributions from everybody. I thought everybody played a pretty solid game tonight, which is good. We need that; we need everybody to do their job out there and contribute in some form.''
Colton Sissons, playing in his 500th NHL game, and Mattias Ekholm scored for Nashville.
The Blues went ahead 1-0 on Schenn's wrister 11 seconds into the second period. The shot caromed off the stick of defenseman Ryan McDonagh and past goalie Juuse Saros.
Schenn scored in overtime to give the Blues a 1-0 victory the previous time the teams played.
The Predators tied it at 2:36 when Sissons was left alone during a bad Blues line change.
''A fast break after a penalty kill,'' Sissons said. ''My linemate (Cole) Smith won the battle in the corner and put it in a really good spot for me on a breakaway.''
Saad put St. Louis back on top with a backhand between Saros' legs at 8:30. St. Louis rookie Tyler Tucker assisted to earn his first NHL point.
''It's nice, obviously,'' Tucker said. ''Saad made a great play there driving the wing and slipped one five-hole. It's nice. Every night you lace them up here you feel more and more comfortable, for sure. It's obviously faster and better hockey. But I thought, so far, that I've made a pretty good adjustment.''
Kyrou also used a backhand to score a power-play goal at 15:34. He has 10 points (five goals, five assists) in nine games against Nashville.
''We played a full 60 tonight,'' Kyrou said. ''I thought we were always attacking, we were playing quick. We were doing a good job of possessing the puck in the O-zone, getting shots to the net, crashing the net. We did a great job tonight.''
The Blues added two quick goals in the third. Thomas scored at 1:03 and Toropchenko followed at 2:01.
''The second (period) was pretty brutal on our part,'' Sissons said. ''They totally took over the game and then had a couple of quick ones in the third and it got away from us.''
Nashville's final goal came from Ekholm at 17:52.
''First period was OK,'' Predators coach John Hynes said. ''They were just a lot better over the last 40.''
A goal by Nashville's Tommy Novak was overturned when officials ruled goaltender interference at 2:03 of the first period. Jeremy Lauzon made contact with Binnington before Novak tapped in a rebound.
''It certainly doesn't help,'' Sissons said. ''It changes the game if we get that one there.''
The Blues had 33 shots on goal. They had been held under 30 for seven straight games. ... Nashville failed on its three power-play chances and is 1 for 24 over its last eight games. ... RW Vladimir Tarasenko (hand), D Torey Krug (lower body), D Robert Bortuzzo (lower body), D Marco Scandella (hip) and LW Logan Brown (upper body) all participated in Thursday morning's optional skate for the Blues. None played against Nashville. ... The Blues wore their white road jerseys at home for the second and final time this season. ... The Predators reassigned D Roland McKeown to the Milwaukee Admirals of the AHL. ... Nashville D Mark Borowiecki (upper body) sat out. ... Blues C Nikita Alexandrov (upper body) is day-to-day.
Predators: Host the Los Angeles Kings on Saturday.
Blues: Host the Chicago Blackhawks on Saturday.
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