Angel Lafita's deflected strike had given the visitors a surprise early lead, but Pepe and a Cristiano Ronaldo penalty put Madrid in front at half-time before Isco and Ronaldo sealed the win in the second-half.
However, it was a frustrating day for Bale, who had been named in the starting line-up, as he was forced to miss what would have been his home debut at the Santiago Bernabeu after injuring his thigh in the warm-up.
"He had a small problem in the warm-up. I don't think it is a big problem, but we have to wait till tomorrow (Monday) to do a scan to see how bad the injury is," said Madrid coach Carlo Ancelotti.
"The player wasn't comfortable, he was worried and so it was better to avoid problems.
"He wasn't happy at the time because he was desperate to play his first game in the Bernabeu, but he has plenty of games ahead of him here."
Isco was drafted in to take the Welshman's place on the left side of a 4-4-2 formation and, despite the disruption, the hosts should still have been in front within three minutes when Ronaldo was denied by two desperate blocks at close range.
The home side were stunned on six minutes though when referee David Fernandez Borbalan waved play on despite Ronaldo's claims for a foul in midfield and Lafita's effort deflected off Pepe past the hopelessly wrong-footed Diego Lopez.
Madrid levelled in the 19th minute as Miguel Angel Moya could only parry Ronaldo's effort from Angel di Maria's free-kick and Pepe bundled home the rebound.
The hosts then went in front 14 minutes later when Michel was harshly penalised for handling Ronaldo's driven free-kick inside the area and the Portuguese confidently dispatched the resulting spot-kick.
Karim Benzema should have given Madrid an even more comfortable half-time lead when presented with a golden opportunity from Dani Carvajal's fine run and cross, but the Frenchman miskicked and Moya was able to make a scrambling save.
Ronaldo had a fierce effort saved by Moya and Di Maria curled a free-kick inches wide as Real looked to put the game to bed at the start of the second period.
Isco did finally give Madrid the two-goal advantage they craved when he ran onto Ronaldo's quickly taken free-kick and bent in his fifth goal in six games since joining the club.
Benzema was met by a chorus of boos by his own fans 18 minutes from time when he somehow headed over Alvaro Arbeloa's inch-perfect cross from just three yards out.
Getafe were then reduced to 10 men when Michel was shown a straight red card for denying substitute Jese Rodriguez a clear goalscoring opportunity five minutes from time.
And the visitors' misery was completed deep into stoppage time when Ronaldo flicked home Sami Khedira's cross to move level with Mexican Hugo Sanchez as the club's fifth highest goalscorer of all-time on 208 goals.
Valencia handed coach Miroslav Djukic a much needed win as they ended a run of four straight defeats with a 3-1 win over Sevilla thanks to a double from Brazilian Jonas Goncalves and Victor Ruiz's late header.
Villarreal continued their unbeaten start to the season, but fell two points behind Real in fourth as they were held to a 0-0 draw at Celta Vigo.
There was also a stalemate in the day's opening game as Real Betis and Granada drew 0-0.