The world's most expensive player added to Asier Illaramendi's first-half opener with a stunning strike on 71 minutes, and then substitute Isco hit a third with 10 minutes remaining.
Although Madrid never hit top gear, they pulled off their 10th home win of the season to keep the pressure on title rivals Barcelona and Atletico Madrid.
In the absence of the suspended Luka Modric, Madrid struggled to control the game in the opening half an hour, their only chances being a blocked effort by Bale, a wayward shot from Angel Di Maria and a miscued effort from Jese, who failed to hit the target after a cutback from Di Maria.
With neither of Madrid's forwards enjoying their finest afternoon, it was left to the man who had been called in to deputise for Modric to get the opener.
Illaramendi controlled a corner with his chest and then fired a low shot into the bottom corner of Manu Herrera's net, to score his first goal for for Real Madrid with what was his first shot in the league this season.
The goal settled Madrid, and Karim Benzema could have got the second before the break, his low shot saved by Elche goalkeeper Manu Herrera.
The visitors had put on a respectable display in the first half but only managed two shots on target throughout the game, and wilted once they went behind.
Herrera almost landed his team in huge trouble when he took the ball round Benzema in his own area and played a hurried pass to Alberto Botia, who was dispossessed by Jese before fouling the Real Madrid forward, but only being shown a yellow card.
Madrid's second goal was certainly worth waiting a little longer for.
Bale had struggled to get involved in the game and had a frustrating first half, giving the ball away on numerous occasions, but soon made amends - picking the ball up around 35 yards out and blasting high into the net to score his 10th league goal for Los Blancos.
Isco replaced the off-colour Jese shortly after Bale's screamer and almost provided the third goal for Dani Carvajal, who completely missed the midfielder's low cut-back from a couple of yards, the ball instead rolling across the goalmouth.
So the former Malaga man took care of the final goal himself, controlling a pass from Benzema then racing between two defenders to knock the ball in at the near post.
And the Bernabeu faithful fully appreciated the youngster's first goal of 2014, greeting the finish by chanting his name loudly.