Nate Smith had booted a 27-yard field goal to put Louisville (6-4, 4-2 C-USA) ahead before Jones missed his fourth field goal in five tries.
Dave Ragone rallied Louisville from a 14-point halftime deficit with touchdown tosses of 13 yards to Joshua Tinch and 34 yards to J.R. Russell, the latter of which tied the contest with 1:16 to play in the third quarter.
Jones missed two potential go-ahead kicks in the fourth quarter, including a 37-yard attempt that was blocked with 1:57 to play.
The Golden Eagles (6-4, 4-2) got the ball first in overtime, but Jones was wide right on a 46-yard try. Louisville running back T.J. Patterson fumbled on the ensuing possession, and nose tackle Rayshun Jones recovered to force a second extra period.
The Cardinals beat the Golden Eagles for the third straight time. Southern Mississippi had won 15 of the prior 17 meetings.
Ragone completed 19-of-37 passes for 200 yards and two touchdowns. For the Eagles, Micky D'Angelo was 17-of-35 for 228 yards and two scoring tosses and one interception.
Chris Johnson caught eight passes for 141 yards, including a 67-yard scoring reception from D'Angelo that put the Golden Eagles ahead, 17-3, with 5:18 to play in the second quarter.
The Golden Eagles outgained the Cardinals, 302-223, but suffered their fourth loss in six games. The teams are one game behind first-place TCU in league play.