Sweden need one win from the remaining two rubbers to reach Saturday's final in Duesseldorf after only the second match in the event's 32-year existence where a player has lost to love.
World number 25 Soderling whipped forehand winners at will against the stunned 32-year-old Schuettler, whose ordeal lasted only 45 minutes.
Red group opponents Germany and Sweden continue their tie with a doubles and singles match on Friday.
France lost 2-1 to the United States, capping a miserable appearance that saw the favourites lose all three group matches. Both teams are already out of contention.
World number nine Jo-Wilfried Tsonga powered back from a set down to beat American Robby Ginepri 3-6, 6-2, 6-4 and level the tie at 1-1 after Sam Querrey earlier beat Gilles Simon 7-5, 6-3.
The Americans snatched the tie when Querrey and Mardy Fish beat Jeremy Chardy and Simon 2-6, 6-4, 10-7. The match was decided on a champions tie-break with the rubber level at one-set all.
In the Blue group, Serbia trail Italy 1-0 after Andreas Seppi beat Viktor Troicki 6-1, 6-4. Serbia must now win the singles and doubles rubbers on Friday to book a spot in the final.