Real will now take on Al Ain in Saturday's final after the United Arab Emirates' outfit got the better of River Plate on penalties on Tuesday evening.
Kashima were regarded as the underdogs to prevail in Abu Dhabi but they almost took the lead as early as the second minute, with Serginho seeing a low effort from 18 yards tipped wide by Thibaut Courtois.
The Japanese outfit went even closer from the resulting corner with Gen Shoji sending a glancing header towards the far corner, only for the ball to evade a teammate and go wide.
However, a succession of half-chances for Real helped them gain a foothold in the contest before the break and although Benzema, Bale and Toni Kroos all failed to trouble Suntae, Santiago Solari's side eventually went in front a minute before half time.
Marcelo had been a threat down the left throughout the first half and, on this occasion, the Brazilian's pass inside found Bale who sent a clinical first-time effort into far corner of the net.
Kashima remained in the game as long as the deficit stayed at one goal, but Real quickly went about ensuring that they could relax for the majority of the second half with two goals in quick succession as Bale completed his hat-trick.
The Welshman's second came as a result of a Kashima mistake with Shuto Yamamoto failing to get the ball back to Suntae, and it gave Bale the chance to get ahead of the goalkeeper before slotting into an empty net with his right foot.
The forward needed just two minutes to make it three. Marcelo was given another chance to tee up Bale and, after taking a touch, the former Tottenham Hotspur man lashed a powerful strike into the far corner of the net.
Solari quickly acted to give Bale the rest of the evening off, but Real remained on the offensive and Lucas Vazquez should have further extended Real's lead only for the Spaniard to fire straight at Suntae when attempting to lift the ball over the goalkeeper.
However, Kashima gave themselves a lifeline with 12 minutes remaining when Doi fired home powerfully from close range, although the goal only stood after being checked by VAR.
Benzema could have added a fourth during the closing stages only to fire wide after latching onto Isco's pass, but Real were still able to comfortably see out the remaining minutes to stay on course for their fourth triumph in this competition.
KASHIMA ANTLERS (4-4-2): Suntae; Nishi (Anzai 56'), Seung-Hyun, Shoji, Yamamoto; Endo (Leandro 81'), Nagaki (Uchida 46'), Leo Silva, Abe; Doi, Serginho
REAL MADRID (4-3-3): Courtois; Carvajal, Ramos, Varane, Marcelo; Kroos, Llorente, Modric; L.Vazquez (Isco 68'), Benzema, Bale (Asensio 60', Casemiro 74')