On the 28th minute, Per Mertesacker heroically thwarted Emmanuel Adebayor from a sure tap-in.
On the 46th minute, Laurent Koscienly flew at Chadli's point-blank range effort to make the decisive block, denying Spurs an equaliser.
After 64 minutes, the Frenchman vitally disturbed Adebayor's bid to turn an inviting cross home.
After 90 minutes, Arsenal were three points behind leaders Chelsea with a game to spare.
Arsenal wore the look of champions at White Hart Lane, efficiently completing the job at hand and finding a way to win.
Arsenal's last league triumph arrived at White Hart Lane ten years ago, on the final day of the 03/04 season as the Invincibles charged to the Premier League crown. The Gunners, as they mount their first genuine challenge for the prestigious trophy since then, affirmed their champions credentials with a champion-like performance to secure a historic derby double over Tottenham, their first since 1980.
The process of grinding out three points has repeatedly been proven successful by the likes of Sir Alex Ferguson and Jose Mourinho in winning titles, and it was a blueprint Wenger adopted here to resist sustained Spurs pressure.
It is implanted in the DNA of champions to produce a poor performance but yet, particularly at an arduous ground similar to White Hart Lane, depart with maximum points secured.
Arsenal have a propensity to deploy attractive football, a wonderful trait to possess but probably not as useful as the grit and character displayed here.
After Rosicky had handed them the advantage with an amazing belter, Arsenal defended stoutly and were superbly organised. Mertesacker and Koscienly continued the defensive solidity they have demonstrated throughout this season with another excellent performance. Emmanuel Adebayor tested the duo thoroughly with his strong physicality and intelligent movement, but the assured centre-half partnership matched the task equally.
Despite the challenges put forward to them, they exuded confidence and look a formidable defensive force to compare with that of Chelsea's - Terry and Cahill.
The Gunners had required only one convicted attack after 73 seconds to ensure victory. Their rivals probed and for all their possession, Szczesny was hardly examined sufficiently. It was indisputably a performance of champions.
His side's performance was surely Mourinho-esque, and so too were Wenger's defensive tactics. The substitutions of Rosicky, Podolski and Chamberlain for Flamini, Monreal and Vermaelen told its own story.
In previous seasons, extensively defensive shake-ups were a rarity for Arsenal as they settled for the top four. But now, serious title contenders, the Gunners have showed signs of their champion potential.
In an excellent season for the Gunners, Wenger has overseen the growth in maturity and character from his side, mixed in with their traditional preferred style of mesmeric one-touch football.
Their venture into the blue side of London to face Jose Mourinho's wounded Chelsea side will prove to be another assessment of their title credentials.