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.
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."
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.
"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."
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.
