Cristiano Ronaldo, Toni Kroos and Marcelo were all rested by Zidane with an eye on Tuesday's first leg in Turin, but Madrid showed no signs of missing their star men at the Estadio de Gran Canaria on Saturday.
Bale put Madrid on track in the 26th minute by running on to a tremendous throughball from Luka Modric and thumping a drive past home goalkeeper Leandro Chichizola.
Benzema struck from 12 yards after Jonathan Calleri brought down Lucas Vazquez in the penalty area and Bale added his 10th club goal of 2018 in all competitions with another spot-kick.
A fourth successive league win moves Madrid within a point of second-placed city rivals Atletico Madrid, who host Deportivo La Coruna on Sunday, but the champions' main focus is on winning a third straight Champions League crown with Barcelona well clear at the top.
Captain Sergio Ramos missed the game with a knock and Nacho Fernandez added to Zidane's defensive injury problems by limping off in the first half, the Spain international left in tears on the bench after appearing to damage his ankle.
Calleri fired a fifth-minute warning shot but his rifled effort flew narrowly wide and Keylor Navas had to dive to his left to push away Alen Halilovic's strike as Las Palmas started well.
Chichizola denied Benzema after the striker ignored the well-placed Vazquez, before the goalkeeper then superbly turned Marco Asensio's shot around the post.
Home goalkeeper Chichizola could do nothing as Madrid took the lead in the 26th minute, though.
Modric's pass sent Bale scampering down the left wing, beating the offside trap, and Wales' newly crowned record goalscorer smashed home a powerful finish.
Madrid's second followed from the penalty spot as Calleri was penalised for a clumsy foul on Vazquez, with Benzema ensuring he celebrated his landmark appearance with a goal by sending Chichizola the wrong way with his spot-kick.
Madrid added to their lead in the 51st minute, Bale coolly converting his side's second penalty of the game after he was caught in the process of shooting by Ximo Navarro.
Benzema unselfishly tried to set his team-mate up for a hat-trick but over hit a simple pass, Alejandro Galvez able to get back and clear Bale's effort from a tight angle off the line, then the striker fired straight at Chichizola from eight yards out when it looked easier to score.
Erik Exposito had a chance to get Las Palmas on the scoresheet but shot wildly over the crossbar after pressing a nervy Navas into a mistake, while Momo saw his header clip the crossbar and Halilovic wasted another opportunity for Paco Jemez's side.
The former Rayo Vallecano coach has now lost on all nine of his meetings with Madrid, who understandably eased off in the closing stages, with attention turning to Turin and Juventus, and Zidane's only concern will be over the extent of Nacho's injury.
