An early goal was all it took for Arsenal to earn a vital win over North London rival Tottenham on Sunday.
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 which 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 home side enjoyed the better of a frantic second period, Spurs could find no way through.
Mesut Ozil's midweek hamstring injury cleared the way for Rosicky to start and he emphatically capitalized with just over a minute played.
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 home side's 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 employer.
But Arsenal retained the greater attacking threat, a fact underlined when Podolski out muscled Younes Kaboul to lash into the side netting.
A smoldering Sherwood, who threw his jacket to the floor in a rage when Oxlade-Chamberlain earlier broke free, sent Tottenham out with renewed vigor for the second period and some haphazard goalkeeping from Wojciech Szczesny almost brought the club level.
Back in the Arsenal lineup 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 was 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.
Koscielny's center 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 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.