The 24-year-old absolutely crushed his groundstrokes as he overpowered a player 12 years his senior to hand Leon Smith's side a very valuable lead in the last-eight encounter.
Edmund's losing run continues in Cologne
Edmund was hugely impressive from the outset, and he closed out the opening set in remarkable fashion as he held serve in just 78 seconds.
The first-set break had come at 3-2 as Edmund capitalised on a succession of sloppy serves from his German opponent.
Kohlschreiber significantly lifted his level and intensity in the second set and he broke Edmund's serve for the only time in the match at 2-1 up.
But the Brit bounced straight back before he seized the initiative again to break and clinch victory from 5-5 with the match in the balance.
Edmund was again seemingly nerveless as he closed out the win before he was mobbed by his team-mates and GB staff on the sideline.
Britain take a 1-0 lead into the remaining two rubbers with Dan Evans taking on Jan-Lennard Struff in the second singles clash.
If required, Britain may need further heroics from Jamie Murray and Neal Skupski in a potentially-decisive doubles rubber.
US Open men
Djokovic bounces back from losing first set to see off Edmund
ATP New York
Britain's Edmund wins New York Open title in straight sets