Having gone scoreless in Madrid's first two wins to start season, Ronaldo headed in Madrid's second goal in first-half injury time to add to Francisco "Isco" Alarcon's 26th-minute opener from Karim Benzema's pass.
Benzema assisted Isco again in the 73rd for his third goal in as many games since joining from Malaga this offseason.
"Things are going well considering we have just started the season, three for three so far," said the 21-year-old Isco. "We are getting better game by game. That's our goal."
Messi started his treble in the 11th when Sergio Busquets intercepted a pass and shuffled the ball to Cesc Fabregas, who then used one touch to send Messi charging into the area and over goalkeeper Diego Alves before rolling the ball home.
The sequence of Busquets robbing the ball, Fabregas assisting, and Messi scoring repeated itself in the 39th.
Barcelona coach Gerardo Martino had said after Barcelona's 0-0 draw against Atletico Madrid earlier this week that he wanted Messi and Neymar to link up more in attack.
Martino got what he had asked for when Neymar picked out Messi arriving down the middle of the area to slice his pass into the net for his league-leading fifth goal in two games after sitting out one match due to a muscle problem.
But just when it appeared Barcelona would romp, Valencia striker Helder Postiga used an acrobatic volley to pull one back in the 44th before he scored with a header from a corner kick in first-half injury time.
Neymar was involved twice more in almost getting Messi another goal, only to see the Argentine miss both late chances before goalkeeper Victor Valdes was forced to tip the shot by Valencia substitute Jonas off his post four minutes from time.
"The concern that Messi and Neymar didn't combine in their first game together, well, they solved that in 24 hours," Martino said.
Barcelona said Busquets ended the match with pain in his right leg and will undergo tests.
Elsewhere, Atletico won 2-1 at Real Sociedad thanks to David Villa's goal in the 27th and assist for Jorge "Koke" Resurreccion to add a second in the 56th.
Sociedad's Xabi Prieto halved the final difference in the 69th in a clash between two teams set to make long-awaited returns to the Champions League.
Atletico, Barcelona, Madrid and promoted Villarreal are the only teams with three wins in as many rounds.
Espanyol, meanwhile, remained unbeaten after drawing 0-0 at home with the winless Real Betis, and Malaga drew 2-2 at Sevilla after Kevin Gameiro equalized twice for the hosts.
Madrid coach Carlo Ancelotti started Diego Lopez instead of Iker Casillas for the third straight match, but the goalkeeper could do nothing to stop substitute Ibai Gomez from getting Bilbao's consolation goal in the 79th.
Ancelotti said that defender Fabio Coentrao was staying at the club after changing his mind over a transfer.
Bilbao midfielder Ander Herrera did not play a day after his club said it had rejected an offer for him from Manchester United. Coach Ernesto Valverde said that his benching had nothing to do with the interest from United and that he expected Herrera to stay.
Before the match started, Madrid dismantled a stage it had set up inside the Santiago Bernabeu Stadium last weekend for Bale's presentation. It will go back up early on Monday for the Wales winger to be paraded in front of his new fans.
Isco poked his first goal under goalkeeper Iago Herrerin after Benzema set him up with a scooped pass made easier by Bilbao's Andoni Iraola who failed to move forward with the rest of the defensive line, leaving Isco onside to take the ball alone in the box.
"Isco is playing very well, it looks like he has been playing here a long time," Ancelotti said.
Ronaldo extended the hosts' lead by running free to head Angel Di Maria's dipping free kick into the corner of the net.
Isco fired in Madrid's third after controlling Benzema's short cross with one touch and scored to ensure Bilbao would suffer its first loss of the season following two victories.
