Chelsea, who have 85 points to Arsenal's 74, will clinch their first title since 1955 with a win at Bolton Wanderers on Saturday no matter what Arsenal do in their last four matches.
Jose Mourinho's side would have been crowned champions if Spurs had prevented Arsenal winning at Highbury.
That rarely looked likely after Spanish striker Jose Antonio Reyes, who missed a first-minute sitter with the goal at his mercy, had rifled Arsenal ahead after 22 minutes after being set free by Francesc Fabregas.
Arsenal continued creating the better chances and Brazilian substitute Edu hit the post during the second half and also fired into the side-netting when it looked easier to score.
However Spurs, desperate for points to boost their hopes of a place in next season's UEFA Cup, were always in contention as they defended resolutely with Michael Dawson outstanding.
Arsenal, playing without injured top scorer Thierry Henry and Fredrik Ljungberg, almost paid for their profligacy in front of goal when Spurs substitute Robbie Keane headed wide from close range three minutes from time.
A goal then would have handed the title to Chelsea, but Arsenal held on to win and stretch their unbeaten run in all matches to 11 and maintain their record of scoring in every home league match this season.
"As long as we have a one percent chance (of keeping the title) we will fight for it," Arsenal manager Arsene Wenger told Sky Sports News. "Our pride is to do as well as we can.
"Today we have 74 points. If you look at any other league we would be top. But Chelsea have got more points and we have to respect that. But it doesn't mean that we have to give up."
