Clear cut chances were few and far between in yet another fiercely contested clash between Liverpool and Everton.
Marouane Fellaini was the first to threaten when he stabbed narrowly wide from Leighton Baines' free-kick on 18 minutes.
With 31 minutes played, Steven Gerrard thought he had opened the scoring. Jordan Henderson teed up his skipper but his close range effort was brilliantly blocked by Phil Jagielka.
Philippe Coutinho opened Everton up when he found Daniel Sturridge in behind, but Tim Howard did well to smother the chance one-on-one on 48 minutes.
The only moment of controversy in the game came 11 minutes after the restart. Baines' corner was headed home at the far post by Distin, but the referee questionably ruled that Victor Anichebe had fouled Pepe Reina in the build up.
Sixteen minutes from time, Coutinho was the architect of another good chance for Liverpool. Gerrard latched on to the youngster's pass, rounded Howard but saw his shot turned off the line by Distin.
The result sees Everton maintain their five point advantage over their rivals in red in sixth and seventh place respectively.