Backup quarterback Blaine Gabbert replaced Mariota before halftime and finished the game 7-of-11 passing for 101 yards and a touchdown.
"It was huge," Titans coach Mike Vrabel said of Gabbert's effort. "That's why he's here. That's his job is to be ready to go, to prepare like a starter -- and then if his opportunity comes, to come in and make the most of it. Really proud of him, really proud of the entire team because they stuck together."
With Tennessee (9-6) fighting for a playoff spot, Gabbert said his mindset was "just go win the game."
"That was really all we were talking about," Gabbert said. "Just get something going on offense. Get some positive plays on first and second down so we can stand third-and-manageable."
Washington defensive tackle Jonathan Allen sacked Mariota for an 8-yard loss before a TV timeout. Mariota landed on his right elbow as he was sacked by Allen.
Mariota went down on one knee as he was coming off the field to talk with Vrabel. The Titans' training staff came onto the field and talked things over with Mariota before he walked off the field and headed straight to the tunnel.
Vrabel said after the game that Mariota was still being evaluated.
The injury occurred with 55 seconds left before halftime. Tennessee was driving but settled for a 42-yard field goal by kicker Ryan Succop after Gabbert was sacked with one second on the clock.
Gabbert said Mariota was "happy" after the win.
"I just told him I always got his back," Gabbert said. "He always works so hard for this football team."