Christen's kick capped a four-play scoring drive that began when UConn (5-6, 2-4 Big East) defensive back Blidi Wreh-Wilson intercepted a pass in the end zone.
Louisville (9-2, 4-2) will have to beat Rutgers Thursday to claim a share of the Big East title.
Christen kicked a field goal in the first quarter and Shakim Phillips caught a 3-yard TD pass in the second overtime that gave the Huskies a 20-13 lead.
DeVante Parker caught a 25-yard TD pass from Cardinals' quarterback Teddy Bridgewater in the second OT to even the score again.
Bridgewater completed 30-of-53 passes for 331 yards, two touchdowns and an interception.
UConn's Chandler Whitmer and Johnny McEntee combined for 92 yards on nine completions.