But he needed kicker Ryan Succop to turn his coach's decision into a 19-17 Titans upset victory over the Chiefs on a 53-yard field goal with no time remaining.
Succop, who was taken by the Chiefs in 2009 as the last player selected in the NFL Draft and spent five years with the team, wasn't sure he could make the kick from that distance because of the weather conditions.
At kickoff, the temperature was one degree with a wind chill making it feel like minus-9. By the end of the game, the actual temperature was nine degrees with a wind chill around zero.
Kicking a football in this type of afternoon is a lot like trying to kick a brick. Succop missed his first attempt from 53 yards, but that played was ruled dead when Chiefs coach Andy Reid tried to ice him with a timeout.
"The first ball I thought I hit well," Succop said. "In those conditions, the ball doesn't travel well. You get no compression.
"When that kick came up just short, there was a moment when I wasn't sure I could even reach it from there."
Succop's second try just creeped over the crossbar and gave the Titans their eighth victory of the season.
"On the second one, I had to throw technique out the window and really go after it and hit it as hard as I could," Succop said. "You could give me 10 kicks from there on a day like today and I don't think I could make one.
"There's only one explanation for why that ball went in today and that's because it was the Lord's will that it go in. I know that was the case."
The Titans (8-6) showed remarkable mettle in the last minutes of the fourth quarter.
With 3:14 to play, Tennessee was down 17-10 but driving for a touchdown. The Titans got the six-pointer as running back Derrick Henry scored his second touchdown of the game, going in from 1 yard to make it a one-point game.
That's when Mularkey decided to gamble, going for two points rather than one on the PAT play.
"I wanted to win, I wanted to win the game right there," Mularkey said of his decision. "Instead of going into overtime, I wanted to make a statement to our team of that"s why we came here."
But quarterback Marcus Mariota was unable to get rid of the ball cleanly, as he was under pressure from the Chiefs' defense. That left the Titans down one-point with 3:12 on the game clock and they did not own any timeouts other than the two-minute warning.
"I think it showed great confidence not only in our defense but our offense and our kicker," Titans tight end Delaine Walker said. "I thought it was a great decision."
Succop bounced the kickoff into the end zone for a touchback and the Chiefs started at their 25-yard line. But as happened throughout the second half, Kansas City couldn't move the ball and stay on the field against the Tennessee defense.
The Chiefs picked up eight yards on three running plays before punting. With 1:07 left, the Titans had the ball at their 25-yard line but no timeouts.
Mariota led Tennessee down the field, completing four of his six passes and picking up two first downs before spiking the ball at the Kansas City 35 with five seconds to play. That brought Succop on the field and the Titans grabbed an improbable victory.
But after 133 yards on nine plays in the first quarter, Kansas City managed just 184 yards on 48 plays the rest of the game. The Chiefs' defense kept them in the game, forcing three turnovers by the Titans, but the offense couldn't do much with the extra opportunities.
"We got three turnovers and to only get seven points out of it is not like us," Reid said. "Red zone was an issue for our offense. We got stopped down there twice (with no points.) When given the opportunity, we've got to make the plays."
But the Chiefs (10-4) produced only a field goal after the first quarter and saw their chance to claim a spot in the AFC playoffs put on hold for another week.
Tennessee cut the margin with a 4-yard touchdown run by Henry late in the first half and picked up a 39-yard field goal from Succop before he kicked the winner.
"Offense, defense, special teams, we all left plays out there that we should have capitalized on," Chiefs linebacker Ramik Wilson said. "But we didn't."
The temperature at kickoff was 1 degree with a wind-chill factor of minus-8. That's the coldest regular-season game in the history of both franchises.
The Titans lost two starters in their secondary in the first half. CB Jason McCourty (chest) and S Da'Norris Searcy (concussion) did not return.