Pierre-Emerick Aubameyang was on hand to put the hosts two goals ahead in the first half, while Robert Lewandowski and debutant Milos Jojic completed the win after the break.
"We played really well," Klopp said. "From the first second we played football as we had planned.
"It was a great football game from us, we scored all the goals at the right time, and that does not happen in every game.
"We won the ball back more often and were able to prevent Frankfurt's deliveries into our area."
The win was Klopp's 111th win as Dortmund boss, equalling Ottmar Hitzfeld's club record, although the 46-year-old downplayed that achievement after the match.
"This is, for me, just a nice number," he added. "When I hear it, I also think of the defeats. We have not won at home for a long time, it could have been 114 victories now.
"What I can say is that I have a great coaching team, Borussia Dortmund is a fantastic club and we always have had good teams."
Dortmund had not won any of its last four fixtures at Signal Iduna Park since the 6-1 hammering of Stuttgart last year.
The win moves BVB to within a point of second-placed Bayer Leverkusen, after Sami Hyypia's side lost to Schalke later on Saturday.