Although United leapfrogged them on Sunday following victory over Liverpool, Chelsea are now back to third place after they could only draw at Blackburn.
However, the Blues have a match in hand and, with just four points separating the top three, could move second again if they beat bottom club Portsmouth at Fratton Park on Wednesday night.
United host Chelsea over the Easter weekend, in between the small matter of the Champions League quarter-finals, and so there is set to be plenty more life yet in what is the most exciting championship race for many seasons.
Almunia, 32, maintains Arsene Wenger's young side have displayed the qualities needed to stay the distance over the final seven matches.
"This team is full of confidence, character, spirit and fight," Almunia told Arsenal TV Online. "It was crucial to win and shows that Arsenal are at the top of the table to fight for the league.
"We will continue to put pressure on them until the end of the season, right up until we have the last possibility to win the league - that is all we can do."
Wenger believes the experience of veteran campaigners such as Almunia, Mikael Silvestre and Sol Campbell - who have all played in either title-winning sides or the Champions League final - will be vital to the success of his emerging squad.
"In the last two months, Almunia has been outstanding, and has come back to his top form. You have to give him credit," the Gunners boss said.
"He kept us in the game on Saturday, and when every player starts to be decisive at some moment in the game, that is a good sign."
Wenger also believes Arsenal have shown they can battle to grind out a result when necessary, having also forced a stoppage-time winner at Hull in their previous match.
"Against West Ham, we saw another side of the team, which is a bit underestimated," he said. "Because we are 'easy' to play, sometimes people underestimate this team has resolve and character.
"What we are doing is outstanding. We know we have not won anything yet, but we are still in the race."
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