Montgomery's score and Riley Patterson's point-after kick brought Detroit back from a 20-14 deficit created by Harrison Butker field goals of 35 and 39 yards late in the third quarter and early in the fourth quarter, respectively.
Jared Goff completed 22 of 35 passes for 253 yards and a touchdown for the Lions, who are a trendy pick to win the NFC Central and did nothing to slow down the hype with a solid performance.
Detroit made few mistakes, committing only four penalties and one turnover.
The Lions' defence came up big in the second half.
Detroit later stopped the Chiefs on their final two possessions after taking the lead.
Mahomes hit on 21 of 39 attempts for 226 yards with a pair of second-quarter touchdowns and one interception.
He also rushed for a team-high 45 yards but had a spate of passes dropped. Kansas City tight end Travis Kelce (knee) was held out of the game.
Getting a rare non-Thanksgiving national television shot after a strong finish to last year nearly produced a play-off berth, Detroit initiated the scoring on Goff's 9-yard touchdown pass to Amon-Ra St. Brown with 2:46 left in the first quarter.
It capped a 14-play, 91-yard drive that lasted just over eight minutes.
Predictably, Kansas City answered with a touchdown march of nearly six minutes. Mahomes connected with rookie Rashee Rice on a 1-yard laser that capped a 13-play drive with 11:50 to go in the second quarter.
The Chiefs took a 14-7 lead with 34 seconds remaining in the half as Mahomes found Blake Bell for a 4-yard score.
Mahomes converted a third-and-17 with a 34-yard strike to Marquez Valdes-Scantling to key the drive.