Cesc Fabregas set the Gunners on their way inside five minutes, as they took a huge step towards qualification from Group H with a third straight win - and their biggest at home in Europe since 1991.
With 12 consecutive victories in all competitions, Arsenal are on their best run of form since their 'Invincible' season of 2003/2004 - and fast closing on an overall club record of 14 in a row set some 20 seasons ago.
Boss Arsene Wenger said: "The players enjoy the way they play, at a high tempo - and that is a joy to watch.
"Overall there is a happiness in the team to play together.
"There is still more to come from this team. Can we keep our humility and feet on the ground? Can we continue to enjoy what we do? Then I feel we can develop.
"We have seen some great performances, but still everyone is improving."
"We just remind everybody that two months ago I was crazy not to buy players and we were not even rated to be in the top seven," Wenger warned.
"We have no reason to be carried away, because exactly the same people who will now say we can win the European Cup said we would finish 15th two months ago.
"We have to be realistic and just prepare for the next game and show we can win it."
Slavia coach Karel Jarolim was left to reflect on one of the worst nights of his career.
"We were not able to do anything about the goals against us," he said. "We let Fabregas in to take the ball without trying - and by the time the third goal went it, that was the beating of us.
"We wanted to finish with some pride in the second half but could not even do that.
"I did not expect we would make it so easy for Arsenal."
Like many others, Jarolim was impressed with Walcott.
"He is a very talented player. We were not able to handle his pace," he concluded.