Arsene Wenger's team had slipped 11 points adrift of Chelsea and six of Manchester United but they recovered strongly in December with four wins and a draw.
Their hopes of moving within a point of the lead on Wednesday were foiled when their home game against Bolton Wanderers was snowed off.
But the Gunners are just two points behind United and four adrift of Chelsea with a game in hand as they seek their first title since 2004.
Home victory over Everton on Saturday would maintain the momentum as Chelsea visit Hull City and Manchester United travel to Birmingham seeking to end City's 12-game unbeaten run.
"We refused to give up. We continued to fight and believed in our strength," Wenger said.
"The biggest test was the mental strength and solidarity of the players. That has been tested. We have a great hunger - it doesn't mean Chelsea and Man United don't - and great team spirit.
"We are a team who have grown up together, we want to achieve things. We haven't won anything yet together and that makes us hungry for success."
Arsenal hammered Everton 6-1 at Goodison Park in a spectacular start to the season but the Toffees have toughened up since and are on a five-game unbeaten run in the League.
A trip to Birmingham would not ordinarily look too daunting for Manchester United but Alex McLeish's team have shown real quality in recent weeks, just as the champions have wobbled with league defeats by Aston Villa and Fulham and to Leeds United in the FA Cup.
UNLIKELY PLACE
Birmingham have climbed to eighth, only five points off an unlikely Champions League place.
"There is an improvement in the league. You have to assess it that way," United manager Alex Ferguson said. "The general standard has improved.
"Look at Birmingham for instance and the fantastic job Alex McLeish has done. What he has done has been marvellous."
United scraped a 1-0 win over Birmingham with a Wayne Rooney goal on the opening day of the season and Ferguson would be delighted with a repeat.
Chelsea's lead has been whittled down by draws with Everton, West Ham United and Birmingham and defeat at Manchester City, though confidence was restored with an impressive Cup 5-0 demolition of Watford.
The Londoners needed two goals from Didier Drogba for their opening day 2-1 home win over Hull but they will have to do without the striker who is on African Nations Cup duty.
Daniel Sturridge made a good start as a replacement when he scored twice against Watford and with Nicolas Anelka likely to miss out again through injury, the 20-year-old should again lead the line.
The battle for fourth place takes centre stage on Sunday when Tottenham Hotspur, who currently occupy it, visit Liverpool, who desperately covet it.
