Los Blancos entered the match having lost on each of their last three league visits to Sevilla, and the home side once again proved far too strong during the 90 minutes of action.
Sevilla were absolutely full of it, and it was not a surprise when they made the breakthrough in the 17th minute through on-loan AC Milan forward Silva.
Jesus Navas was a menace to Los Blancos early on, and it was his pin-point cross that Silva converted to send the home side ahead against the struggling visitors.
Sevilla then doubled their lead in the 21st minute, and the same two players were involved. A quick break from the home side ended with Navas bringing a smart save from Courtois, but Silva was on hand to convert the rebound.
Sevilla almost had a third in the 33rd minute when Franco Vazquez curled one towards the top corner, but the crossbar came to Real Madrid's rescue as the away side just about stayed in the match.
The home side did make it 3-0 in the 39th minute, however, when Ben Yedder placed an excellent volley past Courtois from close range to make it six goals in his last three matches.
Bale should have had one back for the away side just before the half-time break, but the Welshman fired over the crossbar from close range after Sevilla had failed to clear a corner.
It was the first time that Real Madrid had conceded three times in the first half of a La Liga match for nine years, but head coach Julen Lopetegui decided against making changes at the break.
Bale struck wide of the Sevilla post in the 52nd minute as Real Madrid looked to answer back, and the visitors thought that they had registered less than one minute later through Luka Modric.
Indeed, Modric found the back of the net with a super finish from inside the Sevilla box, but the Croatian's effort was chalked off following a VAR review.
Modric brought a smart save from Sevilla goalkeeper Tomas Vaclik moments later, before the home side had two chances of their own to score a fourth - Pablo Sarabia bringing a smart save from Courtois, and Arana having a strike blocked by Bale.
Vaclik made a stunning stop to prevent Bale from registering just past the hour, before the Wales international struck another effort wide of the post four minutes later.
Mariano Diaz was next to try his luck for the away side in the 71st minute, but the summer arrival from Lyon saw the ball fly over the crossbar.
Real Madrid's night went from bad to worse in the final 15 minutes when Marcelo limped off the field with a calf problem, which could rule him out of this weekend's Madrid derby with Atletico Madrid.
Vazquez should have made it four for Sevilla in the 80th minute, but the number 22 somehow fired over the crossbar from close range.
As it transpired, there were no goals in the second period, with Sevilla's sensational first-half performance seeing them collect all three points against an off-colour Real Madrid.
SEVILLA (3-5-2): Vaclik; Carrico, Kjaer, Gomez; Navas, Banega (Mesa 91'), Sarabia, Arana (Nolito 85'); Vazquez; Silva, Ben Yedder (Promes 70')
REAL MADRID (4-3-3): Courtois; Nacho (Lucas 59'), Ramos, Varane, Marcelo; Modric (Ceballos 71'), Casemiro, Kroos; Bale, Benzema (Mariano 59'), Asensio