Saturday's 2-1 loss at Bayern Munich was a fifth straight Bundesliga defeat for Jurgen Klopp's side.
However, Dortmund put their domestic problems behind them by making it four wins from four in Group D following victories over Arsenal, Anderlecht and a 4-0 romp in Istanbul two weeks ago.
This was a tighter affair in the opening stages as a strong contingent of Galatasaray fans helped create a great atmosphere at Signal Iduna Park.
But Dortmund held their nerve as Reus beat the offside trap to net in the 39th minute and Sokratis Papastathopoulos added a second soon after half-time.
Hakan Balta briefly got the visitors back in it, only for substitute Ciro Immobile to put the hosts in control again and a Semih Kaya own goal compounded Galatasaray's misery.
Galatasaray may also face a UEFA inquest after play twice had to be halted briefly due to flares and firecrackers being thrown onto the pitch by the away supporters.
Dortmund were without Mats Hummels, Nuri Sahin, Marian Sarr and Ji Dong-won through injury, while Oliver Kirch and Jakub Blaszczykowski were also absent due to a lack of match fitness.
Galatasaray had Aydin Yılmaz sidelined with a foot problem, but Felipe Melo had sufficiently recovered from a thigh strain to make the starting line-up and Umut Bulut was preferred to Burak Yilmaz up front.
The visitors had an early penalty appeal turned down when Bulut went to ground too easily after making contact with Erik Durm and Wesley Sneijder's overhead kick was comfortably saved by Roman Weidenfeller.
Dortmund then went close to breaking the deadlock after 25 minutes when Papastathopoulos headed against the crossbar from a Reus corner, while Shinji Kagawa was just wide when curling one in with the outside of his right foot.
The hosts went ahead six minutes before the break, though, when Lukasz Piszczek's fine throughball picked out a great run from Reus in behind the Galatasaray backline and the playmaker coolly slotted past Fernando Muslera.
Sneijder almost caught Weidenfeller napping with a snapshot at the start of the second period, but Dortmund were in control when Galatasaray failed to clear a cross and Sebastian Kehl headed down for Papastathopoulos to hook the ball home.
The Turkish side pulled one back after 69 minutes when Balta headed in a Sneijder corner, but Dortmund then broke away through Pierre-Emerick Aubameyang and his cross was clinically chested down and forced past the outrushing goalkeeper by Immobile.
Aubameyang almost added another for Dortmund on the counter-attack, but the fourth did come when an Immobile cross deflected in off Kaya for an own goal.
