Substitute Hiroki Abe sealed the comeback with the third goal in the 84th minute, setting up a semi-final against European champions Real Madrid on Wednesday.
Kashima's Ryota Nagaki cancelled out Angel Zaldivar's early opener soon after the break before Serginho made it 2-1 with a penalty and Abe extended the lead before a late own goal.
Guadalajara, the CONCACAF champions, took the lead in the third minute when forward Zaldivar headed a Javier Lopez cross into the top corner of the net.
Kashima goalkeeper Kwoun Suntae saved a close-range Zaldivar strike in the 40th minute after the Asian champions failed to clear the penalty area from a deep Guadalajara throw-in.
The Mexicans had another chance to go two goals up moments later when midfielder Orbelin Pineda hit the bar with a shot from outside the box in the 45th minute.
Kashima started with greater intensity in the second half, levelling in the 49th when Nagaki put away Shoma Doi's pass.
Brazilian Serginho sent Guadalajara goalkeeper Raul Gudino the wrong way from the penalty spot to put the Asian champions ahead in the 69th minute.
Abe's strike from the left-hand side of the box into the top corner made the score more comfortable for the Asian champions.
Guadalajara got back to 3-2 in the dying minutes when Kashima's Leo Silva put the ball into his own net after Suntae had saved an Alan Pulido penalty awarded by VAR.
Wednesday's clash between the European and Asian champions will be a rematch of the 2016 Club World Cup final when Real Madrid beat Kashima 4-2 after extra time.
"This match is going to garner a lot of attention," said Kashima coach Go Oiwa. "We'll play aggressively and we'll play our own football from the very beginning against Real Madrid."
Home side Al Ain FC take on African champions Esperance of Tunisia in the second of two quarter-finals at the Hazza Bin Zayed Stadium on Saturday. The winners will face South American champions River Plate in Tuesday’s semi-final.
(Reporting by Alexander Cornwell; Editing by Ken Ferris)
