The Brazilian striker's first-half penalty was cancelled out by Villarreal skipper Mateo Musacchio in the early stages of the second period.
However, the former Santos forward struck 20 minutes from time to secure all the points for the Catalan outfit.
Here, Sports Mole dissects the 90 minutes of action between the two La Liga rivals.
On target: 7
On target: 1
Was the result fair?
In truth, Barcelona deserved to pick up all three points this evening. Villarreal were not overly concerned until the latter stages, but the away side managed just one attempt on target throughout the 90 minutes. The Spanish champions were not at their best for long periods, but ultimately it is another three points for the league leaders against a well-drilled and hard-working Villarreal team.
The Catalan outfit might have collected all three points this evening, but they are still not firing on all cylinders, despite a late flurry of chances. Villarreal were comfortable in the first half and for large periods of the second, but Barca did improve considerably when Xavi entered the field on the hour mark. They might be without a certain Lionel Messi, but Neymar has really found some form in the last couple of weeks. Their problems in defence, especially from set pieces, remain, but they have such a wealth of attacking talent in the final third.
The Yellow Submarine have already taken points off Atletico Madrid and Real Madrid this season and it did appear that they were heading for another positive result against Barcelona. Indeed, they were the team who pushed for a second when the score was level at 1-1, but they really struggled for possession in the latter stages. They managed just two attempts throughout the 90 minutes, which was the major disappointment, but the newly-promoted outfit were without arguably their two best players - Cani and Bruno.
Sports Mole's man of the match
Xavi: Neymar might have scored twice this evening, but Xavi is the main reason why Barcelona managed to collect all the points. The home side struggled for invention until the 61st minute, when Xavi was finally introduced. Simply put, the Spanish international changed the entire tempo in the middle of the park. He might be 33, but he remains such a key player for the La Liga leaders.
Biggest gaffe of the match
Barcelona's troubles from set pieces are well known and Villarreal certainly made use of that knowledge this evening. The Yellow Submarine equalised in the early stages of the second half when Musacchio headed home from a corner, but the marking from the Catalan outfit was non-existent. They certainly miss a dominant figure in the middle of their back four.
Ignacio Iglesias handed Barcelona a first-half penalty when Villarreal defender Mario Gaspar handled inside the box, although it was an extremely harsh decision. However, aside from that, the Spanish official was hardly seen as he allowed the match to flow in the right areas, although he did issue a number of questionable bookings in the second half.
Barcelona: The Catalan outfit are in Copa del Rey action on Tuesday as they face Cartagena in the second leg of their fourth-round clash - leading 4-1 from the first leg last week.
Villarreal: The Yellow Submarine are also in Copa del Rey action on Tuesday as they travel to Elche for the second leg of their fourth-round clash. The score is level at 2-2 from the first leg last week.