Everton showed why they are currently ahead of Liverpool in the table with a battling display as they came from two goals to earn a share of the spoils.
Liverpool will feel hard done by as the impressive Luis Suarez controversially had what would have been a winning goal chalked off for offside after a late, late call from the referee's assistant.
Everton welcomed back key man Marouane Fellaini after missing the last two games through injury.
Steven Naismith started for Everton in place of the suspended Steven Pienaar, while Victor Anichebe missed out completely.
Brendan Rodgers sprung a surprise with Brad Jones keeping his place in goal with Pepe Reina named on the bench.
Jose Enrique came into the defence as Glen Johnson missed out through injury.
For Everton it was the usual 4-4-1-1 formation as Moyes was able to welcome back Fellaini into his side in his role behind lone frontman Nikica Jelavic.
In the absence of Pienaar, Kevin Mirallas switched to the left-side of midfield with Naismith slotting in on the right and Phil Neville and Leon Osman in the engine room.
Rodgers stuck to his tried and trusted 4-3-3 formation with Enrique starting at left back and Suso and Sterling supporting Suarez in attack.
The Liverpool boss made a tactical change at the break reverting to a three-man defence with five across midfield and two up front and it seemed to give his side more solidity.
Everton were forced into a change at the start of the second when the impressive Mirallas was forced off with an injury and he was replaced by Magaye Gueye.
Bryan Oviedo came on for the final five minutes for Naismith to stiffen up Everton's left-hand side, but had little time to make an impact.
Rodgers made two changes at the interval bringing on Sebastian Coates for the ineffective Sahin to move to a three-man defence to try and combat Everton's aerial bombardment. Jonjoy Shelvey also came on for Suso to stiffen the midfield with the young Spaniard struggling to make an impact in the first half. Jordan Henderson was also introduced for the final 20 minutes for Andre Wisdom with the youngster finding it tough going down Liverpool's right side.
Andre Marriner had a fairly good game, but he was let down by his assistant in the disallowing of Suarez's last-gasp goal. Quite how he thought Suarez was offside is difficult to tell as the striker was level when he fired the ball past Tim Howard and he made his decision so late as Suarez was already away celebrating the goal. As you would expect in a Merseyside derby it was a hard-fought contest and he dished out seven bookings in the game - four to Everton and three to Liverpool.
Suarez was at the centre of everything that Liverpool did as he played a major role in the first goal as his shot was deflected into his own net by the unfortunate Leighton Baines. The Uruguyan then scored the second himself with a header from Steven Gerrard's brilliant free-kick. Suarez was then extremely unfortunate not to have grabbed the winner when his late strike was controversially ruled out for offside.
Mirallas was Everton's brightest attacker in the first half, causing Andre Wisdom all sorts of problems. Unfortunately for Everton he was forced off at half-time through injury and as a result Everton did not show as much attacking threat in the second period. A notable mention also goes to Leon Osman for an all-action display in midfield capped with a goal.
There are positives to take for both sides from the game. Everton can point to their battling spirit as they came from two goals down to earn a 2-2 draw to keep them six points clear of their local rivals.
It is three draws on the spin for Everton in the Premier League and Moyes will be keen to get back to winning ways soon if they are to challenge for a top four finish this season.
Liverpool will look back at the final result with regret, but again there were positives to take for Brendan Rodgers' side.
After racing into a 2-0 lead, Liverpool should have defended better to stop Everton finding a way back into the contest, but before the game they would probably have taken a point.
Rodgers is now getting the players to play in the style he demands and if Liverpool can get more goals from around the pitch they should soon start picking up more points to climb up the table.