The Brazil forward, who cost 57 million euros ($79 million) from Santos, netted the opener and set up Alexis Sanchez for the second in a 2-1 win at the Nou Camp as the La Liga champions moved six points clear of their arch-rivals at the top.
Wales winger Bale, by contrast, who became the world's most expensive player when he arrived from Tottenham Hotspur for 100 million euros, blazed a couple of long-distance shots over the bar and did little else before being substituted on the hour.
The 24-year-old, who made way for France striker Karim Benzema, was working his way back from injury in only his second start but coach Carlo Ancelotti and Real's demanding fans will expect him to justify his price tag sooner rather than later.
"These are his first games and he needs to find passing combinations with the other players, it's normal," Ancelotti told a post-match news conference.
"He played a good match," added the Italian, like Bale getting his first taste of Spain's 'Clasico' after taking over from Jose Mourinho. "In the overall work of the team he wasn't bad."
Neymar, with the benefit of playing more consistently from the start of the season, has comfortably settled into Barca's team without the need to make up for lost time like Bale who missed nearly all of pre-season through injury.
The 21-year-old Neymar appears more patient and composed, waiting for his moments to excel rather than forcing them, and he has quickly proven he can step up on the big occasion.
He helped Barca win the Spanish Super Cup against Atletico Madrid at the start of the season when he came off the bench to head the equaliser in a 1-1 first-leg draw at the Calderon.
The goal proved decisive as Barca won the trophy on the away goals rule after a 0-0 draw at the Nou Camp in the second leg.
Coach Gerardo Martino said Neymar's performance against Real on Saturday did not rank as his best of the season.
"He played a good game but I believe he has played better ones," the Argentine told a news conference. "He stood out more in this game because he scored."
Bale will have a chance to impress the Bernabeu faithful when Real host Sevilla in La Liga on Wednesday, after Barca play at Celta Vigo on Tuesday.
($1 = 0.7250 euros)