Kagawa set up both the first and fourth goals for Dortmund, plus netted one of his own, while Goetze scored twice as defending champions Dortmund romped to an impressive home win.
Borussia's win puts them second and trims Munich's lead to two points at the top of the Bundesliga with Bayern to play bottom side Augsburg on Sunday.
The hosts took the lead after just 13 minutes as Kagawa took the ball from a throw-in and played Germany play-maker Mario Goezte into the penalty area for the 19-year-old to rifle his shot into the bottom left-hand corner.
Kagawa made it 2-0 just before half-time when he was played into space by Poland striker Robert Lewandowski and the Japanese winger fired past Wolfsburg goalkeeper Diego Benaglio.
Former Arsenal and Barcelona star Aliaksandr Hleb, who was making only his second appearance after signing for Wolfsburg at the start of the season, kept 2009 German champion Wolves in the hunt with a goal on 59 minutes.
But a header from Dortmund midfielder Sven Bender on 61 minutes put Dortmund back into a 3-1 lead before Kagawa produced a defence-splitting pass from deep which put Lewandowski free to fire past Benaglio on 66 minutes.
Goetze completed the rout from a final pass by Bender on 78 minutes as Dortmund look to be back to their best after a slow start to the season.
Werder Bremen went third and joined Dortmund and Borussia Moenchengladbach on 23 points when they came back from 2-0 down to win 3-2 against ten-man Cologne thanks to a second-half hat-trick from Peru's Claudio Pizarro.
Cologne enjoyed a 2-0 half-time lead, but having scored his 150th Bundesliga goal the week before, 33-year-old ex-Chelsea star Pizarro made the difference.
He netted his first goal just after the break, then converted a penalty on 54 minutes after Cologne's Portuguese defender Henrique Sereno was sent off for a foul in the penalty area on Sweden striker Markus Rosenberg.
Pizarro wrapped up his hat-trick four minutes from time when Rosenberg's pass found him at the far post.
Moenchengladbach moved up to fourth after their come-back win at Hertha Berlin as Bayern-target Marco Reus scored both their goals in a 2-1 win.
Colombia striker Adrian Ramos put Hertha into the lead on 18 minutes, but 'Gladbach fought back as Reus netted either side of half-time to leave him with seven goals from 12 league games.
Schalke can jump from fifth to second if they beat Hanover 96 on Sunday.
Hosts Nuremberg lost 2-1 at home to Freiburg as Senegal striker Papiss Ciss converted a penalty with the last kick of the game for the guests which moves them to up third from bottom as mid-table Hoffenheim drew 1-1 with Kaiserslautern.