Bale signed one of the most lucrative deals in football history on Monday to keep him at the European champions until 2021.
Barcelona can close to within two points at the top, but face a huge challenge when they travel to fourth-placed Sevilla later on Sunday.
Bale also scored Real’s fastest ever Champions League goal in midweek against Legia Warsaw, but his fine strike in the Polish capital was forgotten as Real blew a two-goal lead to draw 3-3.
There was to no such comeback from La Liga newcomers Leganes on their first ever league visit to the Santiago Bernabeu after Bale had awoken Madrid from their slumber in the first 30 minutes. Bale outsprinted the Leganes defence as he latched onto Isco’s through ball and rounded Jon Ander Serantes before slotting home from a narrow angle.
His second was a scrappier finish as Bale pounced on a loose ball inside the area from Toni Kroos’s free-kick to bundle home from close range. Serantes prevented Bale completing his hat-trick twice within a minute at the start of the second period.
Bale’s decision to go alone with his first effort infuriated the off-colour Cristiano Ronaldo, who was waiting for the ball to be squared.
Ronaldo endured another frustrating afternoon as he was kept scoreless for the fifth time in eight La Liga appearances this season. The Portuguese was also booked early on for taking his protests towards referee Miguel Mateu Lahoz too far.
Real received a huge boost ahead of a hugely demanding two-month stretch after the upcoming international break as Luka Modric made his return as a second-half substitute after a month out due to knee surgery.
Morata rounded off a comfortable afternoon for Zinedine Zidane’s men when he collected Kroos’s pass before firing home at the near post. And Madrid even kept their first clean sheet in 11 matches as victory stretches their unbeaten run in all competitions to 28 games.