Bale was making his first start at the Santiago Bernabeu and made an immediate impact as he put the hosts 2-0 up within half an hour.
Ronaldo then added a third, but Sevilla fought back through an Ivan Rakitic penalty and Carlos Bacca.
Bale then set up Karim Benzema and Ronaldo to put Real 5-2 ahead before Rakitic replied once more with a stunning strike for Sevilla, although he was to blot his copybook by missing a penalty later.
Ronaldo went on to complete his hat-trick and Benzema rounded off the scoring after Sevilla had been reduced to 10 men when Stephane Mbia was sent-off with 14 minutes remaining.
Xabi Alonso also made his first appearance of the season as a second-half substitute to round off a fine evening for Madrid.
And he believes Bale's brace could be his launching pad to take La Liga by storm.
"He needed a settling in period to the league because it is different to the Premier League.
"We too needed to get to know him, but I am sure that he will keep improving."
Real boss Carlo Ancelotti had made four changes to the side that lost 2-1 to Barcelona at the weekend with Benzema restored to the number nine role between Ronaldo and Bale in attack.
And the Frenchman proved his worth in the move for the opener as he raced onto Isco's pass before cutting the ball back for Bale to fire high into the net on his favoured left foot.
Bale was credited with his second of the evening on 27 minutes when his free-kick took a huge deflection off the arm of Alberto Moreno and looped into the net past the helpless Beto.
Five minutes later it was 3-0 when Isco was unnecessarily dragged down inside the area by Fernando Navarro.
Ronaldo stepped up to fire home and celebrated with a military salute in a mocking response to Sepp Blatter's description of him as a "commander" last week.
"I didn't see the celebration because I was on the bench at the time," added Alonso.
"But he did well in treating it with irony because he is above all these things."
Yet somehow Sevilla were back in the game before half-time when firstly Sergio Ramos was harshly penalised for a push on Diogo Figueiras and Rakitic converted the resulting penalty.
And two minutes later Vitolo ghosted past Alvaro Arbeloa on the right and squared for Bacca to roll into an empty net.
Sevilla could even have been level just after the break when Jairo was denied by Diego Lopez when clean through on goal.
However, seconds later a trademark Madrid break saw Ronaldo feed Bale and his cut-back was calmly slotted home by Benzema for his first goal in eight games.
Bale then provided his second assist of the evening seven minutes later as his low cross was swept home by Ronaldo.
Even at 5-2 the action was far from over as Bale was lucky to escape a booking when he threw himself to the ground looking for a penalty moments later.
And with the Real crowd still infuriated by the referee's decision not to award a penalty for that incident, Rakitic curled in a wonderful effort from outside the box to make it 5-3.
Ronaldo made the game safe when he sealed his hat-trick with a deflected effort from the edge of the area.
Rakitic, though, should have completed hat-trick of his own when Ronaldo was penalised for a foul on Figueiras just inside the area, but the Croat ballooned his second spot-kick well over the bar.
The visitors were reduced to 10 men shortly after when Mbia was shown a second yellow card after clashing with Luka Modric.
And Benzema rounded off a wild night when he headed home Marcelo's cross 11 minutes from time.