Japan midfielder Kagawa rejoined Dortmund towards the end of the transfer window after an underwhelming two-year spell in the Premier League with Manchester United.
The 25-year-old received a marvellous reception from Dortmund fans on his return and it did not take him long to make an impact.
Adrian Ramos broke the deadlock in the 34th minute as he steered Kevin Grosskreutz's low cross into the net and Kagawa ensured Dortmund were two up at half-time.
Ramos played a low delivery into the area and Kagawa arrived late, squeezing his effort just inside the left-hand post.
Pierre-Emerick Aubameyang put the result beyond Freiburg 12 minutes from time as he raced through on goal and chipped a clever finish over the approaching goalkeeper.
Oliver Sorg pulled one back for the visitors in second-half stoppage time, but it was not enough to deny Dortmund a straightforward win.
Schalke coach Jens Keller is back under pressure after his side lost 4-1 against Borussia Monchengladbach at Andre Hahn-inspired Monchengladbach, their third defeat of the season in all competitions.
Hahn opened the scoring with 17 minutes gone, racing free down the right before slamming a finish into the roof of the net and the close-season arrival from Augsburg doubled his tally just after the break when he nodded in Max Kruse's free-kick delivery.
Eric Choupo-Moting pulled one back from the penalty spot in the 52nd minute after Martin Stranzl handled the ball, but Kruse restored the home side's two-goal lead a few moments later after a fine throughball from Raffael and the Brazilian completed the scoring with an easy finish 11 minutes from the end.
Franck Ribery marked his return from injury with a goal as Bayern Munich continued their unbeaten start to the season with a routine 2-0 win at home to Stuttgart.
Mario Gotze opened the scoring in the 27th minute by blasting a low effort past Sven Ulreich in the Stuttgart goal after the visitors failed to clear a corner and, although Bayern were made to wait, they eventually got a second late on.
Robert Lewandowski spotted Ribery in space to his left and the Frenchman calmly slotted past the on-rushing Ulreich, moving champions Bayern on to seven points.
Wolfsburg salvaged a 1-1 draw at Hoffenheim in dramatic circumstances, as Ivica Olic equalised in the 89th minute.
Anthony Modeste put the hosts ahead nine minutes into the second half when he beat the Wolfsburg offside trap, latched on to a lofted ball and beat Diego Benaglio.
However, Olic struck a few moments from the end as he guided Daniel Caligiuri's low cross beyond Oliver Baumann and although Joshua Guilavogui received a second yellow card soon after, Wolfsburg held on for a point.
A double from Shinji Okazaki helped Mainz to an impressive 3-1 win at Hertha Berlin, with Sami Allagui also netting against his former side - who registered through a late Ronny penalty.
Cologne's encouraging start to life back in the top-flight continued as they drew 0-0 at another promoted side in Paderborn, with Peter Stoger's men claiming a third successive cleansheet.
