Hofer made 15 saves in the third period, including a point-blank stop on Tim Stutzle with nine seconds remaining to preserve the lead.
Jake Neighbours scored twice for the Blues (10-12-7), who defeated the Senators for the second time in eight days (also 4-3 at Enterprise Center on Nov. 28).
Fabian Zetterlund scored, and Linus Ullmark made 18 saves for the Senators (13-11-4), who have lost four of their past five games.
Blues forward Jordan Kyrou left the game at 2:52 of the first period with a lower-body injury after taking a hit from Senators forward Stephen Halliday.
Ottawa outshot St. Louis 15-2 in the first. The Senators were 0-for-4 in on the power play in the period and 1-for-7 for the game.
Neighbours gave the Blues a 1-0 lead at 17:36 of the second period, four seconds after a St. Louis power play expired. Brayden Schenn’s one-timer hit the right post, but Neighbours batted the puck out of the air on a drive into the crease.
Neighbours scored his second goal of the game 12 seconds into the third to give St. Louis a 2-0 lead. He tapped in a centering pass from Pavel Buchnevich at the edge of the crease.
Zetterlund cut it to 2-1 at 15:39, one-timing a quick pass from Halliday in the slow slot past a sprawling Hofer on the Senators’ seventh power play of the game.
Ullmark, who was headed off the ice for the extra attacker, dove back to make a desperation stick save on Robert Thomas with the net empty at 18:07.
