Tottenham Hotspur 2 Arsenal 1
Arsene Wenger's side needed to take maximum points from their final five games if they were to stand any chance of winning the league, but they look set to end another season without major silverware once again as they are six points behind leaders Chelsea with just four games to play.
In stark contrast, it was a night to remember for Spurs, who finally put to bed a dismal record which had seen them go 20 league games without a win over their north London rivals.
After losing the FA Cup semi-final against Portsmouth last Sunday, this was the perfect way for Harry Redknapp's team to bounce back.
Rose was making his first league start for Tottenham and will never forget his memorable volley which put the side in front.
Bale added a second before Nicklas Bendtner made it a nervy finish when he pulled a goal back for Arsenal, but Spurs held on to record a crucial victory.
It could have been a different story if Arsenal had opened the scoring inside the opening 60 seconds.
Sol Campbell, who received a hostile reception on his return to White Hart Lane, almost silenced the Tottenham boo-boys when his shot was cleared off the line by Benoit Assou-Ekotto.
Tottenham made Campbell and Arsenal pay when they opened the scoring in spectacular fashion after ten minutes.
Bale's corner was poorly punched away by Manuel Almunia straight into the path of 19-year-old Rose, who fired an unstoppable 30-yard volley past the keeper and into the roof of the net.
It was an extra special moment for the former Leeds midfielder who was celebrating his full league debut in a north London derby.
Arsenal suffered a major injury blow on 18 minutes when Thomas Vermaelen was forced to leave the field after injuring his ankle and was replaced by Mikael Silvestre.
The move clearly affected the Gunners backline and Tottenham could have added a second on 39 minutes when Luka Modric forced his way past Gael Clichy and Silvestre, but saw his shot well blocked by Almunia.
Wenger must have been hoping for an improved performance from his Arsenal side in the second half.
But it was Tottenham who got off to a dream start in the second when they added a second on 47 minutes.
Jermain Defoe raced away down the left and crossed the ball into Bale who was clearly played onside by Bacary Sagna.
The Wales international slotted the ball past Almunia for his first goal of the season and put Spurs firmly in the driving seat.
Arsenal were determined to force their way back into the game and came close to pulling a goal back on 65 minutes, when Bendtner fired a blistering right-foot shot which flew inches past the post.
Wenger brought on Robin van Persie who has been sidelined for the last five months with an ankle injury and he almost made an immediate impact on 80 minutes when his close-range shot was superbly tipped over the bar by Heurelho Gomes.
Gomes came to Tottenham's rescue once again just minutes later when he tipped Campbell's header onto the bar.
Arsenal were handed a major lifeline on 84 minutes when Theo Walcott burst clear down the right and crossed the ball in to Bendtner, who turned the ball home from close range.
But Tottenham held on and are now just one point behind Manchester City as they look to bring Champions League football to White Hart Lane next season for the first time in the club's history.