The Cowboys improved to a 12-4 record after capitalising on a series of penalties to lead from start to finish, leaving them hot on the trail of the 13-2 Philadelphia Eagles in their division.
Mike McCarthy's team must now defeat the Washington Commanders in the final game and hope the Eagles lose both of their remaining two to claim top spot.
Prescott threw both touchdown passes for Dalton Schultz, but also stretched his run to six games with an interception, giving up two in the second quarter as the Titans rallied to 10-6 at half-time with two Randy Bullock field goals.
"A win's a win, and we're going to take it and we're going to get better from the mistakes and make sure that we're improving," said Prescott.
"But a road win, short week, you've got to take them all. And style points and all that, that's for all of you who think games are won on paper."
Asked about the preparations required for the Cowboys' potentially pivotal clash with the Commanders, Prescott added: "Obviously get the rest we need, get our bodies back underneath us and then mentally understanding what's to come.
"Take a couple of days or two and get away from it, but know when we come back we've got to finish this season off on the right foot and we've got a long, long run ahead of us that we know we're capable of making."
Prescott completed 29 of 41 attempts for 282 yards with two TDs and two interceptions, tying Troy Aikman with 165 passing TDs for second most in franchise history.
While McCarthy recognised some shortcomings in the team's performance, much like Prescott he was just content to put another win on the board, particularly with a growing injury list.
"I'm in tune with the injuries and all the things that are going on," he said. "All the little stuff. Yeah, it wasn't clean. This was not a clean performance. We recognise that. I'm not disputing that at all.
"But I do know my football team. I know that they came out of a hard victory on Sunday and took a little longer to get their bodies back.
"That's what Thursday night football is. It's a tough challenge. But the most important thing is we answered the bell and we got it done."