It was the European champions’ first league game in the post Cristiano Ronaldo era, and they rose to the occasion.
Bale crashed a diving header against the crossbar early on, then helped to set up Dani Carvajal’s looping header which broke the deadlock in the 20th minute.
The Wales captain then wrapped up the points with a powerful first-time finish early in the second half, winning a standing ovation by the home supporters later on.
It was his first competitive game back at the Santiago Bernabeu since scoring twice in the 3-1 win over Liverpool in the 2017/2018 UEFA Champions League final.
The result lifts the pressure on new coach Julen Lopetegui after Wednesday’s painful 4-2 defeat to Atletico Madrid in the UEFA Super Cup.
It also sees Real join champions Barcelona on three points after one game, although Sevilla lead the standings on goal difference after their 4-1 win at Rayo Vallecano.
Sevilla forward Andre Silva became the first player since Romario in 1993 to bag a hat-trick in his La Liga debut.
He helped Sevilla to thrash Rayo and scoring the first goal to be awarded in the Spanish top flight with the use of video technology (VAR).
Top-flight debutants Huesca sprang a surprise by winning 2-1 at Eibar.
“It was very important to make a strong start with good sensations and we played very well; we have to go little by little but this is the right way to start the league season,” Real winger Marco Asensio told reporters.
“Cristiano has left but we have a good team. We are working hard, as reflected on the pitch today and this is the way to continue.”
Lopetegui again chose Costa Rica international Keylor Navas in goal ahead of 30-million-euro (26.90 million pounds) signing Thibaut Courtois.
He also fielded Spanish midfielder Dani Ceballos over Luka Modric, who was also left out of the starting line-up in the Super Cup game but came on in the second half.
Real monopolised the ball with a staggering 78 percent of possession and barely conceded a chance to Getafe.
The visitors picked up seven yellow cards as they desperately tried to halt Real’s frequent attacks.
Real’s first clear chance came when Marcelo picked out Bale with a searching cross and the Wales forward dived to meet it but could only head against the bar.
He missed the chance to score his side’s opening goal of the season for a fourth year in a row, with the honour falling to Spain defender Carvajal.
Carvajal stayed with his feet on the ground to head the loose ball into the top corner after Getafe goalkeeper David Soria had flapped at Bale’s cross.
Spanish winger Asensio joined Bale in hitting the woodwork and was also the catalyst for Real’s second goal.
He chased down Getafe defender Djene Dakonam to win back the ball and cross for Bale to hammer it in off the post.
Franco Vazquez had put Sevilla ahead at Rayo before Silva demonstrated the goalscoring prowess which convinced AC Milan to pay 38 million euros for the Portugal international last season.
Silva, 22, scored only two goals in 24 Serie A appearances before joining Sevilla this month but quickly matched that tally by netting twice before halftime.
He completed his hat-trick in the 79th minute with another close-range strike.