Dortmund have led the way since September but BVB's 3-1 win at home to struggling Stuttgart was not enough to keep top spot.
Robert Lewandowski struck twice while Serge Gnabry, James Rodriguez, Thomas Muller and Joshua Kimmich also scored in a comprehensive win against Wolfsburg.
Bayern's comprehensive victory meant they moved above Dortmund on goal difference, with the title rivals having the same number of points with nine games to go.
And Kovac, who was under pressure earlier in the campaign but has steered Bayern back on track, felt Bayern could have secured an even more decisive success.
"I'm very happy with the game, I really liked the way it was and never got in trouble," Kovac said after Bayern's 12th win in 13 Bundesliga games.
"We could and should have scored more goals. That was a good sequel to the Gladbach game [last week's 5-1 victory over Borussia Monchengladbach].
"We are now where we wanted to be in the top of the table - we want to stay there. But nothing has happened yet, there are still many games to go."
Former Bayern player Bruno Labaddia was left to watch on helpless from the bench as substitute Franck Ribery created three late goals off the bench to set a Bundesliga record.
That followed Lewandowski surpassing another ex-Bayern figure in Claudio Pizarro to become the most prolific non-German goalscorer in Bundesliga history as Bayern warmed up for their last-16 Champions League clash with Liverpool in style.
Labaddia has now lost his last 15 competitive matches against Bayern as a coach, a record in the Bundesliga, and he could make no excuses for Wolfsburg's display after their fine run of form ended.
"We do not have to talk about it," he said. "We have seen a very, very strong side of Bayern and a weak team of us. The result was fair.
"Much has not worked out as we usually do. We did not work as a collective. We have to accept that, even if it hurts."