Arsenal put on a magical display at the Emirates Stadium as they closed in on the Champions League knockout stages.
Walcott got his second and third goals for Arsenal
Cesc Fabregas's stunning strike put the Gunners ahead after five minutes and David Hubacek's own goal made it 2-0.
Theo Walcott got his first Champions League goal after a goalkeeping error before Alexander Hleb scored one and set up Walcott for his second.
Fabregas finished a fabulous move and substitute Nicklas Bendtner wrapped up Arsenal's best ever home win in Europe.
The margin of victory also equalled the biggest win in the Champions League, matching Juventus' 2003 demolition of Olympiakos.
It was a simply breathtaking performance from the in-form Gunners, who recorded their 12th successive victory and matched their best result under Arsene Wenger.
Wenger, who celebrated his 58th birthday on Monday, rewarded Walcott for his eye-catching cameo at the weekend with a first Champions League start and he responded in style.
The 18-year-old, who started up front alongside Emmanuel Adebayor, had a quiet opening 20 minutes as his team-mates continued in the dazzling form they have shown all season.
Emmanuel Eboue's pace caused havoc down the right, Hleb was outstanding on the left while Fabregas pulled the strings in the middle.
Hleb's trickery took him to the byeline and he cut the ball back for Fabregas to lift a perfectly-placed shot beyond keeper Martin Vaniak as Arsenal took the lead inside five minutes.
Slavia fashioned a rare chance when David Kalivoda fired narrowly over the bar before Arsenal made it 2-0.
The visitors failed to clear a corner and Hleb's powerful strike took a heavy deflection off Hubacek's outstretched leg to beat Vaniak.
Hleb, Walcott and Fabregas were all on the scoresheet against Slavia
Walcott's first telling contribution came after 28 minutes when he delivered an inviting cross for his strike partner, but Adebayor could only head straight at the keeper.
A little over 10 minutes later, the striker became the youngest Englishman to score a Champions League goal - eclipsing Wayne Rooney.
Daniel Pudil played his keeper into trouble with an ambitious backpass and Vaniak's attempted clearance went straight to Walcott.
The teenager still had plenty to do though, coolly sidestepping Vaniak before firing a precise shot in between two covering defenders.
Desperate Slavia coach Karel Jarolim made a change at the break but Arsenal's response was simply to find another gear.
Hleb got the goal his performance deserved from Fabregas's perfect pass and the Belarussian then set up Walcott, who raced down the left channel before stroking home with the outside of his right foot.
It was a sumptuous finish - reminiscent of Thierry Henry - but the best was yet to come from Arsenal.
Slavia could - and did - only stand and admire as the Gunners went from defence to attack in a flash, the ball gliding from Hleb to Adebayor and on to Walcott before the teenager set up Fabregas to provide the gloss finish.
Those three goals in 13 thrilling minutes of the second-half put Arsenal 6-0 up and Wenger, not surprisingly, made a triple change, introducing Gilberto, Bendtner and Tomas Rosicky for Adebayor, Hleb and Mathieu Flamini.
The changes disrupted Arsenal's rhythm and brought welcome respite to the demoralised Slavia players.
They even had a chance when William Gallas's slip let in Stanislav Vlcek, but Manuel Almunia made a smart save.
Walcott came agonisingly close to a hat-trick but was denied from six yards by a remarkable save from Vaniak - before Rosicky fired the rebound against the bar.
Arsenal eventually got their seventh when Bendtner played a one-two with Eboue, who backheeled his return for the Dane to poke the ball home at the second attempt.
Arsenal boss Arsene Wenger:
"We wanted three points and to play well but you can't predict that.
"Everything went for us. We scored the first goal with the first chance.
"I wanted Theo to start in a big game and he played well. He is calm and clinical in front of goal."
Arsenal: Almunia, Sagna, Toure, Gallas, Clichy, Eboue, Fabregas, Flamini (Silva 62), Hleb (Rosicky 62), Adebayor (Bendtner 62), Walcott.
Subs Not Used: Lehmann, Diaby, Diarra, Eduardo.
Booked: Flamini, Clichy, Hleb.
Goals: Fabregas 5, Hubacek 24 og, Walcott 41, Hleb 51, Walcott 55, Fabregas 58, Bendtner 89.
Slavia Prague: Vaniak, Krajcik, Suchy, Hubacek, Pudil, Senkerik, Svec, Tavares (Belaid 62), Kalivoda (Jablonsky 46), Ivana (Volesak 56), Vlcek.
Subs Not Used: Vorel, Gaucho, Drizd'al, Sourek.
Ref: Stefano Farina (Italy).