The Czech substitute finished off a flowing move with a deflected shot to grab a point for the hosts after Steven Pienaar's superb breakaway goal 11 minutes earlier looked to have won it for Everton in a second-half snowstorm.
Chelsea, who had their trip to Hull City postponed, top the table with 45 points.
Arsenal had won four and drawn one of their last five league games and crushed Everton 6-1 at Goodison Park on the opening day of the season.
However, David Moyes' team are enjoying their own good run at the moment and were far tougher opposition this time.
DONOVAN DEBUT
The visitors took the lead after 12 minutes when U.S. international Landon Donovan, making his debut after joining on a short-term loan this week, swung over a corner and Leon Osman produced an excellent leap to power in a header.
Arsenal levelled after 28 minutes when Denilson's 25-metre shot deflected off Osman and beyond wrong-footed keeper Tim Howard.
Everton survived plenty of pressure as the snow made conditions awkward in the second half and then took the lead nine minutes from time when Tim Cahill sent Pienaar clear and the South Africa midfielder beat Manuel Almunia with a cool, dinked finish.
Almunia prevented a third Everton goal with a good save from James Vaughan before Arsenal roared back into the attack as another neat passing move left Rosicky clear and his shot was deflected past the unfortunate Howard.
The goal brought relief to the frozen home fans but, having seen his team claw their way back from an 11-point deficit five weeks ago, manager Arsene Wenger is likely to see the result as a missed opportunity.
