Dortmund started the day two points clear of Bayern, but Lucien Favre’s side were dismantled during an astonishing first half that saw them concede four times.
Mats Hummels, Robert Lewandowski – with his 200th goal in the Bundesliga – Javi Martinez and Serge Gnabry all scored before the break as the Dortmund defence disintegrated.
Lewandowski added a fifth against his old club for good measure in the final minute to eclipse Gerd Muller’s 14-goal record in ‘Der Klassiker’ fixtures.
“We played perfectly over the 90 minutes,” Bayern boss Kovac said in an interview broadcast on www.bundesliga.com.
“I think you can say it’s a deserved result, but we could have and should have won by a greater mark when you look at the chances and corners we had.
“We showed in every department what I want to see, what I expect, what the benchmark is.
“It was the way we played at the start of the season, and we showed that again.”
Champions Bayern were nine points adrift of Dortmund in December and their grip on the trophy appeared to be loosening.
But Kovac’s side are now one point ahead with six games of the season remaining and in the driving seat to retain the title.
“The first half in particular was sensationally good in every respect,” Kovac added.
“But we still have six matches to go, and you saw how fast it can change in the league.
“Very, very difficult matches are awaiting both Dortmund and us, so we won’t say everything’s decided.”
Dortmund had won their three previous games to suggest that they were firmly back on track following a poor run through February and the start of March.
But their young defence was torn apart and the gulf between the two sides looked enormous, even though Mahmoud Dahoud might have given the visitors an early lead when he struck the woodwork.
“The 5-0 defeat is very, very hard to stomach but it was really deserved,” Dortmund manager Favre said.
“You have to admit it was a lesson. We still had the first chance to score, that could have changed the match a bit.
“Bayern were dominant then, they were quicker, they were better.
“When you’re four down at half-time it’s very hard to bounce back.”