Messi chipped goalkeeper Antonio "Tono" Rodriguez in the 35th minute for his 249th league goal, leaving him two behind the all-time scoring record held by Telmo Zarra since 1955.
A minute later, Neymar added his seventh league goal in as many rounds, giving the strike pair a combined 13 of Barcelona's 19 goals in league play.
"This goes in runs. The connection between (Messi and Neymar) is working for us now and others will appear," Barcelona coach Luis Enrique said.
Barcelona's sixth win, to go with one draw, left it two points ahead of Valencia, after it beat Atletico Madrid 3-1. Atletico's first league loss dropped the defending champion five points adrift of Barcelona and provisionally in third.
Sevilla, Real Madrid and Celta Vigo can all pass it with wins on Sunday.
Also, Eibar scored in injury time to earn a thrilling 3-3 draw with visitors Levante. Malaga rallied for a 2-1 win against visiting Granada, and Almeria drew 2-2 at home with 10-man Elche.
Bravo needed to protect his goal for 20 minutes to break the record set by former Barcelona goalkeeper Pedro Artola, but he had to get low to stop Alberto Bueno from scoring in the eighth.
Rayo coach Paco Jemez insists on an attacking style and a pressing defense, so it seemed only a matter of time before Barcelona took advantage of Rayo's high defensive line.
Moments after Messi had a goal annulled for offside, he broke through when he ran onto Gerard Pique's long ball, held off his marker, and used his left foot to lift the ball over Tono.
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