The Monterrey side have never won the region's premier club competition but, 3-0 up from the first leg, wasted no time in silencing the home crowd with goals from Enner Valencia and Julian Quinones in the first 34 minutes.
Julio Furch got goals back for the home side four minutes before half time and on the hour before Diego Valdes put them 3-2 ahead on the night when he stabbed home a spilled cross with a quarter of an hour remaining.
Man of the Match Quinones hit the post twice for the visitors and Javier Correa missed a penalty for Santos with almost the last kick of the game.
Tigres, runners up to America in 2016 and another Mexican side Pachuca in 2017, will play either city rivals Monterrey or Sporting Kansas City for the title later this month.
Monterrey lead 5-0 after the first leg, making them odds-on favourites to progress after Thursday night's second leg in Kansas.
(Reporting by Andrew Downie, editing by Nick Mulvenney)
