Sylvain Distin had a goal unfairly disallowed as Everton were denied a first league win over Liverpool at Anfield since 1999.
After a frenetic first half low on goalmouth action, Distin thought he had broken the deadlock when he headed home a fierce Leighton Baines corner, but referee Michael Oliver ruled that Victor Anichebe had impeded goalkeeper Pepe Reina.
Liverpool, who had earlier gone close through Daniel Sturridge, responded to the let-off with a spell of sustained pressure in which captain Steven Gerrard had an effort cleared off the line by 35-year-old defender Distin.
The draw leaves Everton in sixth place, five points behind Tottenham, who are occupying the Europa League qualifying place, with two games left for Moyes’s team and three for Spurs.
The Toffees are, however, five points clear of Liverpool and with two games remaining they will expect to finish above their bitter rivals in successive top-flight seasons for the first time since 1937 (not including the several seasons Liverpool spent in the lower leagues of course).
A third 0-0 draw in five matches reflects Liverpool’s lack of adaptability when Plan A goes awry, while Everton were once again shown up for a lack of firepower that has seen them score fewer away goals than any other side in the top eight.
Liverpool carved out the first opening when a typically incisive long pass from Gerrard picked out Sturridge on the left side of the box, and only a diving block from Distin prevented Jordan Henderson from tucking away the striker’s low cross.
Everton took longer to settle into the game but should have taken the lead when Marouane Fellaini was presented with a clear-cut opportunity.
A Baines out swinging free-kick from the left made its way through a crowd of players to the Belgian, whose side-footed effort from well inside the six-yard box drifted past the far post.
Gerrard, had a chance on the half-hour mark but his goal bound shot was blocked well by Phil Jagielka, who had to be at his sharpest soon afterwards to deny Coutinho.
Sturridge, leading the line for Liverpool while the suspended Luis Suarez watched from the stands, had two chances in quick succession shortly after half-time.
Played through on goal by Coutinho, he was brilliantly thwarted by Tim Howard as he attempted to round the American goalkeeper, and when a loose ball fell to Sturridge, he could only find the side-netting with his shot on the turn.
Moyes cut an angry figure as he implored his players to match Liverpool’s second-half energy and his mood was momentarily brightened when the Toffees thought they had taken the lead.
Distin climbed above Jamie Carragher, making his 30th and final Merseyside derby appearance, at the far post to nod in Baines’s corner, but referee Oliver ruled it out because he believed, wrongly, that Anichebe had blocked Reina.
Down at the Kop end, Sturridge then played in Gerrard, who rounded Howard but could not generate enough power to prevent Distin from clearing off the line.
There was no let-up in the tempo as the game entered its final phase, but with too many passes going astray, neither side could open up a path to goal.
The Blue Union MoM was Phil Jagielka
by Ken Billwright