Arsenal produced three stylish goals as they dumped FA Cup holders Liverpool out of the competition with a stubborn and resilient third round performance.
Rosicky showed his lethal side to bag a brace for Arsenal
Tomas Rosicky curled a sublime strike and squeezed in a shot from the edge of the box to put the visitors 2-0 ahead.
Liverpool hit back when Dirk Kuyt glanced in from point-blank range.
But Thierry Henry ended hopes of a Reds comeback when he robbed Jamie Carragher and slotted home to book Arsenal's place in Monday's fourth round draw.
Liverpool had plenty of possession early on but Arsenal had kept them at arm's length while waiting for the chance to counter-attack.
The home side were being denied the space and time to create a chance and had only a long range Steven Gerrard strike, which went comfortably wide, to show for their early efforts.
Arsenal's ploy almost reaped reward when a clever pass by Robin van Persie was slid into the piercing run of Rosicky, who lacked the bravery to try and squeeze the ball past on-rushing keeper Jerzy Dudek.
The match started to develop into a fractious affair as rash challenges, stray arms and simulation saw play interrupted on a regular basis.
Reds midfielder Xabi Alonso thought he should have had a penalty when he went over after minimal contact by Gilberto Silva tackle but only ended up getting booked for diving.
In amongst the set-pieces, Reds striker Peter Crouch ballooned a volley over and Alonso went close from 20-yards.
Arsenal had a strength to their play which critics have accused them of lacking and they blended that with the kind of flair they are famed for to take a 2-0 lead.
Dutch striker Kuyt's goal gave Liverpool brief hope
The visitors won possession in their own half and Rosicky exchanged a number of passes with Alexander Hleb down Arsenal's right flank.
The final act of the goal saw Hleb pull a low cross back to the near edge of the box and Rosicky curled a shot into the far side of the Reds goal.
The Czech Republic attacking midfielder added a second when Liverpool's defence stood off him and shot low into the corner.
An urgency in Liverpool's play after the break put Arsenal under relentless pressure.
And, while the visitors threatened on the counter-attack, they started to become overrun by the waves of attacks from the Reds.
The home side's efforts finally told when Kuyt flicked in a header and Aurelio sent an angled volley just wide as Liverpool's dominance was almost rewarded with an equaliser.
But Henry dispossessed Carragher on the left touchline and ran towards goal before cutting inside and sidefooting in to secure Arsenal's win.
Liverpool boss Rafael Benitez:
"It is a bad day for us. It was a difficult game but we were doing well and controlling the match in the first half but conceded two goals.
"It could have been a penalty but for me it is rather the game as a whole.
"We made mistakes and when you play against a good team they punish you. Now we have to think about the next game and keep going."
Arsenal boss Arsene Wenger:
"I felt we have shown character and good discipline. We were organised under pressure.
"We had two or three good chances on the break and scored one - then it was all over.
"They have an unbelievable crowd and the team gave everything. It takes a good team to beat them and we were that team."
Liverpool: Dudek, Finnan, Carragher, Agger, Riise (Aurelio 60), Pennant, Alonso, Gerrard, Luis Garcia, Kuyt, Crouch.
Subs Not Used: Reina, Hyypia, Gonzalez, Bellamy.
Goals: Kuyt 71.
Arsenal: Almunia, Eboue (Hoyte 66), Toure, Senderos, Clichy, Hleb, Silva, Flamini, Rosicky, Henry (Walcott 88), Van Persie (Julio Baptista 72).
Subs Not Used: Poom, Djourou.
Booked: Senderos, Clichy, Eboue.
Goals: Rosicky 37, 45, Henry 84.
Ref: S Bennett (Kent).