Arsenal manager Arsene Wenger expressed his relief after the Gunners needed an 88th-minute winner to beat West Ham.
Robert Green made several fine saves to deny the hosts before Alex Song's late header sealed a dramatic 1-0 victory.
"When you win with two minutes to go, it is always a relief," said Wenger. "We needed to be patient, intelligent and not to make a mistake at the back.
"I was thinking it was one of those days but we kept going and have once again shown a great attitude."
The result keeps Arsenal second in the table, five points adrift of leaders Chelsea after they beat Blackburn at Ewood Park.
It looked as though Wenger's men would have to settle for a draw as Green pulled off a series of brilliant stops to thwart Cesc Fabregas and Theo Walcott, while Samir Nasri rattled the crossbar and Walcott saw a shot come back off the post.
But Arsenal continued to press for the win and they eventually broke West Ham's resilience when Song met Gael Clichy's floated cross with a diving header.
"We did not do anything stupid, kept trying to be intelligent and that got us the goal," stated Wenger, whose side face Shakhtar Donetsk in the Champions League on Wednesday.
"I was thinking it was one of those days when the ball went on to the post and came back into the goalkeeper's hands, that is not a good sign.
"We have matured, you see that in the game the way we handle it when it does not work for us, the players remain calmer than before.
"We have a good chance for the title, yes, but we want to show consistency first. We go step by step and we still need to step up a gear to completely achieve that.
"But on the other hand you feel there is more to come out from this team, we have good potential on the bench today and some players to come back.
"If we can keep a good injury record then we have a chance."
Arsenal claimed a morale-boosting victory over title rivals Manchester City last Sunday and backed it up by brushing aside Newcastle to reach the Carling Cup quarter-finals.
The north London club are bidding to win their first piece of silverware since 2005 and a first league title since 2004 and Wenger is confident they can succeed.
Wenger endured a frustrating afternoon on the touchline
"It is too early in the season, but I have belief," said the Frenchman. "We need to show from game to game we can handle every single game with a different aspect which the Premier League has.
"Today we played against the team bottom of the league and it was a real battle. We have to show we can compete like that in every game."
Wenger hopes captain Fabregas will be fit to travel to Donetsk and revealing the Spaniard may have suffered a recurrence of the hamstring injury that recently kept him out for a month.
"Cesc played a bit within himself. He had a bit of tension in his hamstring. Let's hope he has no setback," added Wenger.
"At half-time, I had a hesitation to take him off. Then I left him on, I thought 'just for 10 or 15 minutes', but in the end he got better and better."
West Ham's defeat leaves them bottom of the table with just one win all season, but boss Avram Grant was pleased with his side's efforts.
The Hammers, who also reached the Carling Cup quarter-finals with an extra-time victory over Stoke in midweek, defended doggedly throughout and looked dangerous on the counter-attack.
"When you come to just two minutes from the end, and it was 0-0, Arsenal almost did not create many chances, because we defended well and played well, so we are very disappointed," said the Israeli, who believes his side can escape the relegation zone.
Grant proud of players despite defeat
"We have played a game against a very good team who just beat us in the last minutes, so we can take a lot of positive things and also from many things which have happened in the past week.
"I don't want to talk about history, whether things are possible or not possible. We are not in a situation where we cannot do it - we can do it.
"We need to win games, we have deserved to win games and will try to do it in the next game [at Birmingham on Saturday]. We are not yet in November, so we have time to do it. There are six or seven months until the end of the season.
"Even if we were in this situation in April, I would not think it was the end of the world."
Grant added: "We are not in a good situation in the league, but we are in a good situation with our performances so we need to take more points like we deserve.
"I really believe we can do it because the team have a good spirit and it was an heroic performance today. We know the difference to us winning games is not so big, so let's continue to fight.
"The players are not giving up, they are fighting, it is a good basis for the future."
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