Real eventually eased their way to victory over the minnows, but they did not have it their own way during the opening quarter of the game as Leganes prevented the home side from having a shot on goal.
When the chances finally arrived, Morata headed over from an acute angle and Cristiano Ronaldo - who had already been booked for dissent - volleyed over from 14 yards out.
The visitors would continue to frustrate the league leaders but with seven minutes to go until half time, the deadlock was finally broken as Bale latched on to a pass from Isco before he rounded Jon Ander Serantes and slotted into an empty net.
Leganes needed to reach the break trailing by just the one goal but with the last kick of the first half, Bale poked home from close range after the ball fell invitingly for him inside the six-yard box.
Real returned for the second half with the intent to quickly find a third, and Bale should have completed his hat-trick when getting himself free inside the penalty area but he put his shot too close to Serantes.
The Leganes stopper then kept out a header from the Welshman as the home side continued to throw men forward, but they failed to kick on and they struggled to create any more opportunities before the match entered the final quarter.
The visitors were never lacking in ambition but they had to wait until the 72nd minute to force a save out of Keylor Navas, who managed to tip Szymanowski's shot over the crossbar after he had run through on goal.
That near miss resulted in Real moving through the gears to net a third goal of the game as Morata benefited from a fine through-ball from Luka Modric before slotting the ball inside the near post from 12 yards.
James Rodriguez and Ronaldo sent late free kicks off target but Real were happy to settle for just the three goals as they strengthened their position at the top of the table.