Making his first home start for the Spanish club, Bale also conjured two assists in a performance that will help dispel doubts about the 100 million euro winger's form and fitness since his record move from Tottenham Hotspur.
France striker Karim Benzema, who has been struggling to find the net for both club and country, also helped himself to two goals as third-placed Real closed to within two points of Atletico Madrid ahead of their game at Granada on Thursday.
Carlo Ancelotti's team looked far from convincing at times and let Sevilla back into the match after taking an early 3-0 lead but what eventually became a rout was a welcome boost after Saturday's 2-1 defeat at Barcelona.
Sevilla played the final quarter of an hour with 10 men after midfielder Stephane M'Bia was shown a second yellow card for catching substitute Luka Modric with a flailing arm and it was the first time in almost 50 years that 10 goals were scored in a La Liga match at the Bernabeu.
"It was quite a strange game with the amount of goals and everything that happened, some of the decisions, but we got the three points," Real midfielder Xabi Alonso, who came on as a second-half substitute after a lengthy injury absence, told Spanish television.
"Personally I am very pleased to be back because these five months have been a big challenge," added the Spain international.
"Little by little I will pick up the pace and start to be useful to the team again."
Bale's pre-season preparations were disrupted by the protracted negotiations over his move and he has gradually been working his way back from a thigh strain in recent weeks.
The 24-year-old fired Real ahead in the 13th minute when he picked up a Benzema pass in the area and lashed the ball superbly into the top corner.
By scoring at Real's giant arena, the Welshman was following in the footsteps of British compatriots Laurie Cunningham, Steve McManaman, David Beckham and Michael Owen.
Bale's second came in the 27th when his free kick ricocheted off Sevilla fullback Alberto Moreno and bounced into the net past wrongfooted goalkeeper Beto.
Real were apparently flying when Isco won a penalty converted by Ronaldo five minutes later but the visitors stunned the home fans into silence with two quick goals.
Ivan Rakitic struck from the penalty spot in the 38th and Carlos Bacca finished off a sweeping move two minutes later to make it 3-2 at the break.
The second half was equally eventful, with Bale setting up first Benzema and then Ronaldo before Rakitic curled a superb shot into the top corner for 5-3.
In a frantic 10 minutes, Ronaldo completed his 18th La Liga hat-trick with a deflected shot, then gave away a penalty that Rakitic fired over the bar before M'Bia was dismissed to end any hopes of a Sevilla comeback.
Benzema netted the final goal of the night 10 minutes from time when he headed home a Marcelo cross from the left.
"It was entertaining for the fans but not so much for the coaches," Real director Emilio Butragueno told Spanish TV.
"They prefer more control and that wasn't the case," added the former Real and Spain striker.
"We have to keep a clean sheet at home. We have to reflect because they had two one-on-ones that Diego Lopez stopped brilliantly and we have to be careful."
Sevilla are 10th on 13 points, the same as 11th-placed Valencia who surrendered a 1-0 advantage to lose 2-1 at home to Almeria, the bottom club's first win of the campaign.
Real Sociedad also blew a lead when they went 2-0 ahead at Real Valladolid before the mid-table clash ended 2-2, while Osasuna thumped fellow strugglers Osasuna 3-1.
Unbeaten league leaders Barca, who won 3-0 at Celta Vigo on Tuesday, have 31 points from 11 matches, with Atletico on 27 and Real on 25.