Indianapolis won the Houston Texans in the AFC Wildcard game scores 21:7.
Dallas will now face either the New Orleans Saints or the Los Angeles Rams in the divisional round.
Marlon Mack, Colts, ran for 148 yards and a touchdown on 24 carries to help Indianapolis top Houston 21-7.
The running back finished with 30 touches for 169 yards as Dallas' defence ended the Seahawks' streak of nine straight victories in playoff opening games. The Elias Sports Bureau said it was the longest streak in National Football League history.
Dallas' defense, ranked in the top 10 most of the season, mostly kept quarterback Russell Wilson under control and handed him his first loss in four wild-card games.
Wilson connected with J.D. McKissic on a seven-yard touchdown pass with 78 seconds remaining and a two-point run put Seattle within the final margin, but Dallas recovered a poor onside kick attempt and ran out the clock.
Brett Maher kicked a 39-yard field goal for Dallas and Sebastian Janikowski answered for Seattle from 27 and 42 yards, but hurt his left leg on a 57-yard miss to end the first half, forcing the Seahawks to chase touchdowns and two-point conversions in the second half.
Prescott made undoubtedly the most spectacular run of the night, with the Cowboys clinging to a 17-14 lead and facing a third-and-14 from the Seattle 17-yard line and the two-minute warning approaching.
Unfortunately, fans have to decide who they'd rather see their team play based purely on their own opinion, as the Patriots haven't faced either team this season.
Dallas' defense came through again, though, forcing a punt and giving Elliott and Prescott a highlight play apiece on a drive to Prescott's 1-yard sneak for a 24-14 lead with 2:08 remaining.
Luck went 19-for-32 for 222 yards, two touchdowns, and one interception in an uneven but productive-enough afternoon at NRG Stadium, powering the Colts to a 21-7 win over the Texans that vaults them from the No. 6 seed to a chance to play in the AFC Championship Game.
The Colts, who opened the season 1-5, continued an impressive run by winning their fifth straight and for the 10th time in 11 games.