The Koreans have played in the last seven tournament finals and the quality of their football at the air-conditioned Al Sadd Stadium suggested they would make it eight in Brazil in 2014.
Striker Lee Keun-ho (twice), defender Kwak Tae-hwi and substitute Kim Shin-wook scored for the visitors who had too much class for a limited Qatar side restricted to counter attacking.
The victory put the Koreans top of Group A alongside Iran with what looks like a straightforward match against the lowest-ranked side left in Asian qualifying, Lebanon, at home on Tuesday.
Qatar took the lead against the run of play in the 22nd minute through a fine individual goal by Yousef Ahmad Ali.
The speedy Saudi Arabian-born striker outpaced defender Kwak down the left, cut in and fired a low shot under goalkeeper Jung Sung-ryong to give the 2022 World Cup hosts a surprise lead.
The Koreans, though, were not rattled and continued their composed pass-and-move style and Kim Bo-kyung's left wing cross was headed in three minutes later at the near post by striker Lee Keun-ho.
The visitors continued to control possession and the pressure told in the 55th minute when Kwak made up for his weak defending earlier to nod in a corner at the near post.
Qatar were enraged 10 minutes later when they went 3-1 down through Korean substitute Kim Shin-wook even though Lee Dong-gook, who provided the assist, looked offside in the build-up.
The hosts lost their discipline in the final stages with a number of rash tackles.
Blond striker Lee Keun-ho was then left unmarked to head his second with 10 minutes remaining after a corner bounced across the goalmouth.
Qatar, who won in Lebanon on Sunday, have little time to dwell on the defeat with an away trip coming up against Iran on Tuesday.