Arsenal ensured a 10th consecutive season in the Champions League group stages as they completed a routine qualifying win over Sparta Prague.
Rosicky's early goal settled any Arsenal nerves
Tomas Rosicky, playing against his former club, put the tie beyond doubt on seven minutes, converting Theo Walcott's cross with a crisp finish.
The Gunners did not need to find top gear, with Sparta offering little.
But Cesc Fabregas's 82nd-minute drive and Eduardo da Silva's last-minute volley confirmed Arsenal's dominance.
Resuming with a 2-0 lead from a bad-tempered first leg, the Gunners wasted no time in trying to put the game beyond Sparta with Robin van Persie heading narrowly over from Gilberto Silva's first-minute cross.
Justin Hoyte's badly underhit backpass - forcing goalkeeper Manuel Almunia to race off his line to clear under pressure from Libor Dosek - provided Sparta with their first half-chance.
But any nerves for the home side were settled when Rosicky's quality goal effectively ended the tie as a contest.
Walcott, played in down the right flank by Hoyte, beat his man easily and sent a low cross into the box which Rosicky met without breaking stride before scoring with a shot underneath the keeper.
The match started to resemble a five-a-side training run-out with Arsenal fizzing the ball around in Sparta's half, but leaving the occasional gap at the back.
Van Persie linked up with the lively Eduardo, and the Dutchman saw his well-struck shot finish just wide of the post.
A largely placid Sparta began to find a little more possession, but clear-cut chances were few and far between.
The best move of the half came from the visitors with a delightful diagonal pass from Pavel Horvath catching Gael Clichy napping, and the Gunners were lucky to see Jan Rezek's lofted effort miss the target.
The start of the second half saw a more aggressive approach from the visitors, although their reluctance to have a shot when the opportunity presented itself gave Almunia a largely trouble-free evening.
Walcott showed some encouraging touches on a rare start
An embarrassingly obvious dive in the penalty area by Horvath went rightly unrewarded, with Kolo Toure's challenge nowhere near the Sparta midfielder.
Arsenal upped the pace a little, with a dissatisfied Arsene Wenger sending on Fabregas and Emmanuel Adebayor to raise the tempo, and a sense of urgency returned.
The hard-working Eduardo pushed the ball past Zdenek Pospech into space, and cut the ball back for Fabregas to power the ball into the net.
Sparta did have the hint of a chance through Daniel Kolar, but he dithered over his shot and saw Clichy take the ball off his toes.
But the last word deservedly went to the Gunners, with Denilson linking up with Adebayor on the right of the box before swinging in an inviting cross for Eduardo to volley home from point-blank range.
Arsenal boss Arsene Wenger:
"We finished the job well by scoring an early goal.
"After that of course it took a little bit of edge out of the game.
"We kept good focus, there's not a lot more to say. You felt always that if needed we could put our foot on the gas and score."
Arsenal: Almunia, Justin Hoyte, Toure, Senderos, Clichy, Walcott, Diaby (Fabregas 68), Silva, Rosicky (Denilson 73), Eduardo, Van Persie (Adebayor 68).
Subs Not Used: Fabianski, Hleb, Flamini, Bendtner.
Goals: Rosicky 7, Fabregas 82, Eduardo 89.
Sparta Prague: Postulka, Repka, Kladrubsky (Limbersky 77), Kadlec, Abraham, Rezek (Kolar 73), Horvath, Pospech, Husek, Kulic (Zofcak 46), Dosek.
Subs Not Used: Kozacik, Brezinsky, Kisel, Slepicka.
Booked: Kulic, Repka, Husek.
Referee: Frank De Bleeckere (Belgium).