The 24-year-old threw for a career-high 442 yards and four touchdowns as the Ravens recovered from a 25-9 deficit to the Colts with just under 12 minutes remaining in the fourth quarter.
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.
He became the first quarterback in the NFL to complete 85% of his passes in a 400-yard game. He became the first player in NFL history with 400 yards passing, four touchdown passes, no interceptions and 50 yards rushing. He also had the highest completion rate in a 40-pass game in NFL history (86% with 37-of-43 attempts).
Ravens head coach John Harbaugh was effusive in his praise afterwards.
"It's one of the greatest performances I've ever seen," he told the media.
The star QB just said he was in the zone.
"I was just locked in," Jackson said. "I was just calm, everything was moving slow. I was just taking it a play at a time."
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.
He told the media he had an "intense stabbing pain" every time he swung his leg, an injury that arose in pre-game warmups.
"Obviously, it affected him, but I give him credit for fighting through it," Colts head coach Frank Reich said. "We didn't have any other answer."
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.