The Gunners made a perfect start and were in front with just five minutes on the clock.
Alexander Hleb found space on the left and held up the play before feeding the ball inside to Cesc Fabregas, who curled a superb right-foot shot into the far corner of the net from just inside the area.
Gael Clichy and Emmanuel Eboue were threatening down the flanks for the Gunners and it was no surprise when they doubled their lead 24 minutes in.
Fabregas' corner from the right caused chaos and when the ball eventually fell at the feet of Hleb, his shot was deflected into the net off defender David Hubacek.
On the half-hour mark it was almost 3-0 as Walcott crossed from the left and Emmanuel Adebayor's header from eight yards was kept out by the boot of keeper Martin Vaniak.
However, Vaniak was at fault four minutes before half-time as he miscontrolled a passback and Walcott sidestepped the keeper to bury his shot from the edge of the area and extend the lead further.
Any concerns of a dull second half were cast aside within six minutes of the restart, as Fabregas found Hleb in space over on the left and he stepped inside his marker to bury a low shot from 15 yards.
It was 5-0 four minutes later as Hleb turned provider to play in Walcott, who coolly slid his shot past the advancing Vaniak into the far corner of the net.
With less than an hour played the Gunners made it six with the goal of the game, Hleb led a superb counter and found Adebayor, who in turn fed Walcott and he put it on a plate for Fabregas to complete a fantastic move.
Slavia threatened to pull a goal back on a couple of occasions, with Manuel Almunia making smart saves from Matej Krajcik and Stanislav Vlcek.
Walcott missed a couple of chances to complete his hat-trick as time ticked away, before sub Nicklas Bendtner rounded off an amazing evening, latching on to Eboue's superb flick the Dane knocked the ball past Vaniak and then rolled it home from a matter of inches.