Jose Antonio Reyes gave Arsenal all three points in the north London derby.
The Spaniard struck midway through the first half when he was played in by Cesc Fabregas on the left and unleashed an unstoppable shot past Paul Robinson.
Patrick Vieira and Philippe Senderos went close with headers and Edu hit the post, while Jens Lehmann made a sharp stop to deny Tottenham's Jermain Defoe.
Spurs substitute Robbie Keane headed wide late on, ensuring Chelsea must wait until Saturday to win the title.
Arsenal are now 11 points behind the champions-elect and all eyes will be on the Blues at Bolton when a win will hand them the Premiership crown.
With that margin now all but unbridgeable, Arsenal will take more satisfaction in that they pulled four points clear of Manchester United in the race for second.
Reyes started in attack with Robin van Persie and the pair linked for the first chance of the game after just 50 seconds.
The Dutchman played in Reyes, but after rounding the keeper he found the angle too acute and his right-footed effort hit the side-netting.
It was a golden opportunity, but Reyes shrugged off the setback and made amends after 22 minutes.
A neat midfield exchange between Fabregas and Vieira finished with the young Spaniard releasing his compatriot and this time Reyes made no mistake, on his favoured left foot, after racing through a static Spurs defence.
It should by rights have been an equaliser.
Arsenal had played over-elaborate football at the back to gift a chance to Defoe, but after creating space to shoot he opted for power over placement and Lehmann stood tall to parry.
That was to prove one of only two clear-cut Spurs chances, the second being Keane's flashing header with four minutes remaining.
Arsenal peppered Robinson's goal but, like the visitors, they only managed one effort on target.
Vieira met a high inswinging Van Persie free-kick at the far post but headed wide, while in the second half Senderos met another Van Persie dead ball with a thumping header over the bar.
Having opened the match at a fierce pace, the Gunners took their foot off the gas after the break.
Tottenham enjoyed more possession but were unable to make any real inroads into the Arsenal massed ranks, who, while less dynamic, maintained a calm, controlled approach.
As time ticked down they sparked life into an increasingly turgid game, Kolo Toure firing a 40-yard free-kick just over while Edu and Reyes hit the post and side-netting respectivley.
Bergkamp curled an effort wide and Erik Edman blocked an Edu shot, but while a second goal would have calmed the nerves, ultimately, it was not needed.
The win gave Arsenal their first league double over Tottenham in 16 years and ensured they hold on to their Premiership crown for at least another five days.
Arsenal manager Arsene Wenger:
"We played some great football against a good, well organised team.
"They fought in a fair way and tried to play as well. We needed an exceptional Arsenal side in patches to win.
"Jose was very lively. He missed an early chance but after he scored he was a different animal. He was a big threat."
Tottenham manager Martin Jol:
"It would have been nice to have a point and we could have had a point with Robbie Keane.
"We did better after the first 20 minutes, when we gave away too much space, and with a bit more conviction we could have had a result.
"They play awfully well at home and when you lose 1-0 you can't be too disappointed, but we could have had a draw."
Arsenal: Lehmann, Lauren, Toure, Senderos, Cole, Fabregas (Edu 70), Silva, Vieira, Pires, Reyes (Aliadiere 88), Van Persie (Bergkamp 69).
Subs Not Used: Campbell, Almunia.
Goals: Reyes 22.
Tottenham: Robinson, Kelly, Dawson, King, Edman, Davies, Davis (Ziegler 79), Carrick, Reid, Kanoute (Mido 70), Defoe (Keane 78).
Subs Not Used: Naybet, Cerny.
Booked: Davis, Edman, Kanoute, Dawson.
Ref: M Riley (W Yorkshire).