Four times this season, Luck and the Colts have erased double-digit deficits and rallied for wins.
Their never-say-die belief was on full display last weekend when the Colts staged one of the greatest comebacks in NFL playoff history, recovering from 28 points down in the third quarter to edge the Kansas City Chiefs 45-44.
The Colts will not want to spot Brady a four touchdown advantage like they did against the Chiefs, especially at Gillette Stadium where the Patriots went an unbeaten 8-0 during the regular season.
Brady was not always at his absolute best but the future Hall of Famer has always saved that for the post-season, recording more playoff games (17) than any other NFL quarterback.
With four touchdown passes against Indianapolis on Saturday, Brady would claim another line in the record books, surpassing Brett Favre and Joe Montana for the most post-season strikes.
"It's incredible to play in this," said Brady, who will try to send the Patriots through to their third straight AFC championship game. "These are the moments you dream about and you have a chance with eight other teams to be the last team standing.
"It's why we work hard. It's why every guy puts a lot out there. You sacrifice a lot of things. A lot of people would die to be in our positions."
Indianapolis and New England are no strangers to the playoff crucible.
The Colts have made the playoffs in 11 of the last 12 seasons, reaching the Super Bowl twice, for one win and a loss. The Patriots have advanced to the posteason in 12 of the last 13 seasons, appearing in five Super Bowls, and claiming three titles.
The experience between Saturday's starting quarterbacks, however, is vast.
While Brady has been under center for each of those playoff games, Luck will be making just his second post-season start.
Both quarterbacks had similar seasons with Brady throwing 25 touchdowns and 11 interceptions while Luck tossed 23 touchdowns and was picked off nine times.
It was a particularly trying campaign for Brady, who has had to work with an almost entirely new supporting cast, after Wes Welker joined the Denver Broncos, Rob Gronkowski was plagued by injuries and Aaron Hernandez was dropped by the Patriots after he was charged over the fatal shooting of a friend.
Brady was still able to work enough of his magic so the Patriots join the post-season well-rested and on a roll, having won five of their last six.
New England's 10th ranked defence will have to deal with the Colts' dynamic young offence, led by Luck and second year wide receiver T.Y. Hilton, who had the best game of his young career against the Chiefs, hauling in 13 catches for 224 yards and two touchdowns.
One of the most intriguing matchups will occur on the sidelines where Indianapolis coach Chuck Pagano will match wits with one of girdiron's top tacticians, Patriots head coach Bill Belichick, whose 18 playoff wins rank third on the all-time list behind Hall of Famers Tom Landry (20) and Don Shula (19).
"He's one of the best in the business and his record obviously speaks for itself," Pagano said about his opposite number. "He does a tremendous job with his football team week in and week out, season after season."