He threw a pair of touchdowns to tight-end Mark Andrews in the fourth quarter to bring the Ravens level.
And although the Colts had their chance to win the game afterwards — kicker Rodrigo Blankenship missed a 47-yard field goal attempt as time expired — Jackson led the Ravens down the field on the first possession of overtime, sealing the memorable victory with a five-yard touchdown pass to Marquise Brown.
On the way to scoring 22 unanswered points against a tiring Colts defense, Jackson entered the record books on three counts.
Ravens head coach John Harbaugh was effusive in his praise afterwards.
The star QB just said he was in the zone.
While the Ravens won their fourth game in a row, for the Colts, it was another disappointing outcome after a promising performance.
Quarterback Carson Wentz — who signed in the offseason from the Philadelphia Eagles — produced his best game in a Colts uniform, completing 25 of 35 passes for 402 yards and two touchdowns.
The Colts running game looked dynamic too, with Jonathan Taylor and Marlon Mack cutting through the Baltimore defense.
However, an injury to the usually reliable Blankenship cost the Colts, as he missed two field goals — including the potential 47-yard game winner — as well as an extra point.
Despite the positive performance, it means the Colts are now 1-4, and third in the AFC South division with a home game against the Houston Texans up next.