Aaron Ramsey thought he had put Arsenal ahead against Liverpool in the ninth minute, but it was ruled offside in a marginal decision.
Arsenal's former Chelsea goalkeeper Petr Cech did well to deny Liverpool's new striker Christian Benteke from close range in the 39th minute after a low cross by Philippe Coutinho.
Coutinho had hit the crossbar in the second minute from Benteke's cutback, and the Brazilian struck the woodwork again just before halftime when Cech tipped his curling shot onto the post.
Brazil forward Roberto Firmino (left) made his first start for Liverpool.
Belgium striker Benteke, signed from Aston Villa, was a constant threat as Liverpool dominated the opening period.
The second half was a different story as Arsenal created chances, Chile striker Alexis Sanchez hitting the outside of the post from a scoring situation.