Veteran quarterback Matt Hasselbeck, making his second start for injured Jake Locker, completed 25-of-44 passes for 290-yards and one touchdown but drew on all his experience with the game on the line.
After the Steelers Shaun Suisham missed on what would have been a career-best 54-yard field goal, Hasselbeck went to work with 49 seconds on the clock and marched the Titans 34-yards, well inside Bironas's range for a shot at the winning kick.
The victory was just the second of the season for the Titans (2-4) while the injury-ravaged Steelers remained winless on the road in falling to 2-3.
"Everyone believed in what we were doing," 37-year-old Hasselbeck, the second oldest quarterback in the National Football League this season, told reporters.
"We knew we had plays there to make, we just had to go do it and not make excuses. It wasn't about the Steelers, they are a good team, it was just about us.
"We're struggling, we weren't doing our assignments, we had mental errors, we were losing the turnover battle. We just needed to fix it.
"We were really sloppy, we still made mistakes but it feels really good to come away with the win."
After trading short field goals off their opening drives, Steelers quarterback Ben Roethlisberger hooked up with Mike Wallace on an 82-yard touchdown pass to put the Steelers 10-3 ahead.
Roethlisberger completed 24-of-40 passes for 363-yards to move past Hall of Famer Terry Bradshaw as the Steelers all-time passing yardage leader.
But the rest of the half belonged to the Titans, Bironas connecting on a 38-yard field goal before Jamie Harper turned a blocked punt into Tennessee's first rushing touchdown of the season, bulling his way into the endzone from the one-yard-line.
The Titans capped off an impressive opening half, converting a Roethlisberger interception into another 47-yard Bironas field goal to send the home side into the intermission 16-10 up.
Pittsburgh opened the second half by scoring on a Suisham 28-yard field goal then followed up with a with an 80-yard drive capped by a one-yard plunge by Baron Batch.
Suisham equaled a career-best with 52-yard field goal to push the Steelers ahead 23-16 early in the fourth quarter before the Titans offence finally clicked, Hasselbeck finding Kenny Britt with a five-yard touchdown strike to level the contest.
"We worked to get this one," said Britt, who had four catches for 62-yards. "We got confidence in our kicker and I knew he was going to pull it out."