Wigan Athletic had the lead twice in the first half through Arouna Kone and Franco di Santo and despite dominating for long periods, they were pegged back by a Nikica Jelavic header and Leighton Baines' late penalty.
Latics put in a powerful first half performance, with Argentine striker Di Santo returning to the starting line-up in place of Jordi Gomez.
It was a game that started with furious pace but, was given a shining start by some patient trickery down the left side by Shaun Maloney.
The Scottish midfielder had the beating of Seamus Coleman who went to ground only for Maloney to skip past and clip his cross to the front post.
In came Kone to thump a header between Tim Howard and the near post at a very acute angle, it was a sensational start from the Ivorian.
Within a breath it was 1-1 when Steven Pienaar's attempted shot ballooned into the air, only for it to drop at the back post and Croatian striker Jelavic poked it in with his head.
Latics weren't to be down-hearted for too long though as they continue to attack time after time.
On 23 minutes they regained the lead when Gary Caldwell's long ball sent Kone on his way in a foot race with Johnny Heitinga and there was only going to be one winner.
Kone raced to the by-line and looked cornered but, his cut-back to the penalty spot was capitalised on beautifully as Di Santo smashed the ball into the roof of the net.
Three minutes later Di Santo almost had another when he cut in from the left side onto his right foot and forced Tim Howard into a finger-tipped save that had the crowd on their feet.
Before the half time whistle Ali Al Habsi was called into action to keep the scores level.
The first chance could have been a cruel deflection as Leon Osman's shot flicked up into the air off Gary Caldwell and looked to be going in over Al Habsi's head but, the Omani stopper leaped to tip it over the bar.
Mirallas then tested the reactions of the goalkeeper as his low, deflected shot into the bottom corner had to be tipped around the post.
Latics' excited attacking play nearly paid dividends when a Kone, Di Santo and Maloney linked up on the counter attack.
Kone played Maloney through on goal and instead of shooting the Scotsman cut the ball back to the Ivorian whose shot was blocked at the last second by Phil Jagielka.
Despite dominance throughout, Latics were caught late on when Maynor Figueroa was penalised for a foul on Kevin Mirallas and a penalty was awarded.
Baines did the honours for Everton to level the scores, a point that Everton may feel a little lucky to have achieved.
Latics should have claimed all three points in the 89th minute when once again Kone played Maloney through on goal.
Maloney took his time to strike as defenders threw themselves in front of him but, when he did pull the trigger the ball ricocheted off two defenders and skimmed the cross bar.
It was the last action of the game and Latics were left frustrated by an Everton side that looked shaky at the back.
Latics: Al Habsi, Boyce, Ramis, Caldwell, Figueroa, Beausejour, McCarthy, McArthur, Maloney, Kone, Di Santo (McManaman 84)
Unused Subs: Pollitt, Jones, Watson, Gomez, Boselli, Miyaichi
Everton: Howard, Coleman, Baines, Heitinga (Distin 45), Jagielka, Neville (Anichebe 81), Osman, Pienaar, Fellaini, Mirallas (Naismith 90+3), Jelavic
Unused Subs: Mucha, Oviedo, Gueye, Duffy