Dynamo, who were in action during the DFB-Pokal, opted for three changes from the side that lost to Arminia BIelefeld. That saw Fabian Müller, Andreas Lambertz and Kutschke replace Nils Kreuzer, Pascal Testroet and Aias Aosman.
Braunschweig were well-rested having last played on Sunday, though Torsten Lieberknecht still made alterations to his line-up as Salim Khelifi and Mirko Boland came in for Christoffer Nyman and Quirin Moll.
Hernandez heads Braunschweig ahead
It was a struggle in the opening stages for both sides but a stroke of luck gave the Lions the first opportunity of the match. A deflected strike from Patrick Schönfeld was deflected into the path of Domi Kumbela. The striker volleyed onto the bar but Hernandez was quickest to the rebound and nodded in from close range for an early lead.
Unfortunately that wasn't the spark that the game needed and the midfield battle for control quickly became the main feature of the match once more. However, Dresden slowly came to life. A superb run from talented youngster, Niklas Hauptmann saw him slalom past several players before firing just past the far post.
Kutschke had the major chances, at that length it is being generous, as Braunschweig seemed happy to stand off their opponents for the remainder of the half. The former VfL Wolfsburg forward headed and shot over and wide, respectively, with Dynamo pushing for an equaliser. It would not come before the break, however.
Kutschke completes remarkable turnaround
Much like the first half, things were tight and tense to begin with but Braunschweig managed to grab another goal at a crucial time. For the hosts it was another case of individual error being the catalyst, as this time Lambertz was robbed of possession. Kumbela was the man to benefit, firing into the bottom corner from the edge of the box.
That seemed to unsettle Dynamo and they had Marwin Schwäbe to thank for making a superb reaction save at the back post, after Nik Omladic's cross ran the while way through to Hernandez. The in-form forward came close again moments later, heading over the bar after another excellent Omladic delivery.
From there, everything changed as Uwe Neuhaus' men took to a new level. Nils Teixeira was given the ball wide on the left and he took most by suprrise with a superb first-time cross into Kutschke. The towering forward finally made a chance count as he swept home in style to leave Jasmin Fejzic with no chance.
Kutschke got his second five minutes later as Fejzic failed to deal with a corner and only succeeded in punching the ball into a Dresden body. It came quickly to the first goalscorer and he made no mistake in finding the far bottom corner. Testroet could have completed the turnaround on the following attack, only for Fejzic to deny him.
The third would come and in the 81st minute Kutschke completed his hat-trick. A superb, driving run from Akaki Gogia provided the space for him to slide the ball into Testroet, and he picked out Kutschke in the middle to finish into an open net. That was the final moment of action, as Dresden somehow came back from the dead.