Suter and McTavish each added an assist, Adam Jiricek scored his first NHL goal, and Pavel Buchnevich had three assists for the Blues (3-2-1), who have won two games in a row and have points in three straight (2-0-1). Joel Hofer made 15 saves.
Claude Giroux and Fabian Zetterlund scored for the Senators (5-2-0), who had won three straight. Samuel Ersson made 19 saves.
Suter gave St. Louis a 1-0 lead with a short-handed goal at 14:28 of the first period. Colton Parayko delivered a strong check along the wall in the Blues’ defensive zone to force a turnover, then fed Suter on the rush, before he went in alone and beat Ersson from the left hash marks.
Neighbours extended the lead to 2-0 at 13:20 of the second period with a shot from the high slot.
Giroux cut the deficit to 2-1 at 17:52. Tim Stutzle battled for the puck behind the net before winning possession along the goal line and sending a backhand pass to Giroux in the right face-off circle, where he snapped a wrist shot high to the blocker side.
McTavish restored the two-goal lead 33 seconds later, making it 3-1 at 18:25. Jonatan Berggren found McTavish surrounded by three Senators players just outside the crease, where he backhanded the puck into the open net.
Suter made it 4-1 at 7:54 of the third period with his second of the game, scoring from a sharp angle with a one-timer that snuck under the right arm of Ersson.
Neighbours pushed it to 5-1 with his second of the night at 14:46, tapping in a feed from Buchnevich on the rush.
Less than a minute later, McTavish got his second of the game with a shot from the right circle on the power play to make it 6-1 at 15:33.
Jiricek, playing his sixth NHL game, extended it to 7-1 at 16:32, beating Ersson from just above the right circle.
Zetterlund scored on the power play at 18:33 for the 7-2 final.