Roethlisberger became Pittsburgh's career passing yards leader, breaking a record held by four-time Super Bowl-winning quarterback Terry Bradshaw, but the fourth field goal of the game by Bironas created the upset.
Tennessee improved to 2-4 while the Steelers dropped to 2-3.
Roethlisberger threw for 363 yards, giving him 28,066 for a career that is in its ninth season. Bradshaw had 27,989 yards in 14 seasons.
Pittsburgh took the lead early in the fourth quarter on a 1-yard run by Baron Batch at the end of an 80-yard drive and Shaun Suisham increased the Steelers' advantage to 23-16 with 8:18 to go by kicking a 52-yard field goal.
Matt Hasselbeck, filling in as Tennessee quarterback for the injured Jake Locker, then drove the Titans 80 yards and threw a 5-yard scoring pass to Kenny Britt that tied the contest with 4:19 remaining.
Suisham had a chance to put Pittsburgh back in front, but his 54-yard attempt with just under a minute to go came up short. That gave the Titans a chance to win it and they took advantage -- the key play coming when Hasselbeck hit Jared Cook with a 25-yard throw to the Pittsburgh 25 with 39 seconds remaining.
Hasselbeck was 25-of-44 for 290 yards while Bironas kicked field goals of 22, 38 and 47 yards in addition to his game-winner.
Roethlisberger's only touchdown pass was an 82-yarder to Mike Wallace in the first period that gave the Steelers a 10-3 lead.
Notable deaths of 2014 [PHOTOS]