The Czech midfielder struck in just the second minute to pour more misery on Tim Sherwood's men, as the Gunners moved level on points with second-placed Liverpool
The Czech smashed home a superb strike, after good work from Alex Oxlade-Chamberlain, in just the second minute to seal victory and pour more misery on Tim Sherwood's men.
It represented a worst-case scenario for a Spurs team who came into the game on the back of moral-sapping defeats to Chelsea and Benfica, along with a pre-match fan protest against chairman Daniel Levy.
The superb Oxlade-Chamberlain and Lukas Podolski passed up chances to increase Tottenham's misery and, although the hosts enjoyed the better of a frantic second period, they could find no way through.
|VIEW FROM WHITE HART LANE
|By Greg Stobart at White Hart Lane
The Arsenal players knew how much this win meant and it showed as they took selfies on the White Hart Lane pitch in front of their celebrating away supporters. This was a victory they did not deserve on the basis of a below-par performance - but it was borne of resilience and grit as they kept their title hopes alive by beating their greatest rivals.
Tomas Rosicky’s goal was a worthy matchwinner, a stunning half-volley that was in the back of the net before anyone in the stadium had any idea what he was doing. Spurs huffed and puffed and should have equalised in the second half through Nacer Chadli but Tim Sherwood must accept that this north London derby defeat has killed Tottenham’s top-four ambitions.
Oxlade-Chamberlain - operating in central midfield as he did so impressively against Bayern - broke up play to feed Rosicky to his right. In trying to collect a return pass, he miscontrolled but the ball fell perfectly into the Czech playmaker's path and a blistering half-volley whistled into the top corner.
In the 15th minute, Oxlade-Chamberlain then skipped around Nabil Bentaleb and was granted a clear path to goal by Tottenham's perilously high line - but dragged an attempted chip wastefully wide.
Andros Townsend, making only his second league start for Tottenham since November, drove to the byline to clip across the face of goal before Oxlade-Chamberlain was once again off target in the 27th minute after Podolski found the hosts' makeshift back four to his liking.
Emmanuel Adebayor, who scored twice the last time that Arsenal won at White Hart Lane in the league in September 2007, got in front of Per Mertesacker to prod Kyle Naughton's cross past the post for his current employers.
But Arsenal retained the greater attacking threat, a fact underlined when Podolski outmuscled Younes Kaboul to lash into the side netting.
A smouldering Sherwood, who threw his jacket to the floor in a rage when Oxlade-Chamberlain earlier broke free, sent Tottenham out with renewed vigour for the second period and some haphazard goalkeeping from Wojciech Szczesny almost brought them level.
Back in the Arsenal line-up following his European ban, Szczesny dropped two crosses in quick succession - the latter dropping to Nacer Chadli, whose shot was blocked on the line by Laurent Koscielny.
The Belgium international came close again in the 53rd minute, missing out on the decisive touch when Adebayor allowed Townsend to again flash a dangerous ball across the Arsenal goalmouth.
Tottenham were now in the ascendancy and looking to bombard the Arsenal box from wide areas. Koscielny had to be on his mettle once more, harrying Adebayor into heading wide.
And Koscielny's centre-back colleague Mertesacker was fantastically denied by Hugo Lloris at the other end in the 78th minute, before their defensive alliance ensured Arsene Wenger's side closed to within four points of leaders Chelsea with a game in hand.
Seven points behind Manchester City having played three games more, Tottenham's once realistic top-four ambitions now appear slim.