The draw took Everton to 14 points from six matches before their rivals play this weekend with a top-of-the-table clash that sees leaders Manchester City, who have a maximum 18 points, visiting Tottenham Hotspur in second on 14.
"It's a good point in the end. We defended set plays and second balls well against a difficult team," said Everton manager Ronald Koeman. "The team performance was outstanding, although we'd like to create more opportunities.
"We've had a good start to the season. The position in the table is not everything at the moment and we need to improve, but we're doing a good job."
Having lost their unbeaten league record at Bournemouth last weekend, Everton looked hungry to make amends and, propelled by the fleet-footed Yannick Bolasie playing against his former club, they quickly took the initiative.
A Bolasie cross came close to picking out Lukaku at the far post after 14 minutes before the Belgium targetman did make his mark on the scoreboard 10 minutes before the break.
He bent a superb free kick over the wall after Damien Delaney was penalised for a high boot on Phil Jagielka, although the Everton defender had handled the ball as he raised both arms to protect himself.
"I have chased the ball and put my head in," said Jagielka. "I got a bit scared and tried to protect myself and ended up handballing it. It is a natural reaction to a high boot. The ref knew that. It was his decision."
Alan Pardew thought his Palace side were hard done by with the foul given against them. "I was a bit disappointed that the referee gave the free-kick. It was a bit harsh," he said.
Palace have proved lucky opponents for Lukaku, who has scored four goals in his last five top-flight appearances against the south London side who stay in seventh spot.
However, his Belgium team mate Benteke denied Everton the victory when he powered a header past helpless goalkeeper Maarten Stekelenburg from Joel Ward's cross.
He has now scored five goals in six games against Everton.
There were nine yellow cards handed out at Goodison Park -- the most in the top flight this season -- but it was more competitive than dirty as both sides battled for points in another of this season's Friday night matches.
(Writing by Ken Ferris; editing by Martyn Herman)
