Critical of the court earlier in the week, Schuettler and his Argentine opponent struggled to find their rhythm in the two hour 25 minute Red Group clash.
Two of ATP's most athletic and improved players, the fourth-ranked Coria and sixth-ranked Schuettler produced an energetic effort under a hot Texas sun but after nearly two months of indoor tennis appeared to struggle with the outdoor elements.
It is the first time the ATP has staged its year-end event outdoors since 1974 when the finale was held in Australia.
"It was strange," admitted Schuettler, runner-up to Andre Agassi at this year's Australian Open. "All three sets had an early break."
"Of course it's a change to play outdoors again."
"To be honest, it was tough to get a rhythm today because it was a little bit windy."
"The sun was low so from side to side I had trouble serving. But I was fighting hard and at the end the fighting paid off."
Certainly the newly constructed $10 million court appeared to the 27-year-old German's liking early in the opening set as he stormed to a 3-0 lead.
But Coria quickly responded with a three-game run of his own to level the contest before Schuettler embarked on another three-game run to take the set.
The streaky play continued into the second but this time with 21-year-old Coria leading 3-0 on his way to levelling the match at a set each.
The first German to qualify for the year-end event since Nicolas Kiefer in 1999, Schuettler again struck a rich vein of form in the third.
He broke Coria to open set then rolled to a 4-1 lead from which the Argentine could not recover.
"I'm proud to be there for the first time and play in the Masters Cup," said Schuettler, the second oldest player in the elite eight-man field after 33-year-old Agassi. "I've had a great season and I'm very happy to have won my first match."
"Now I can enjoy myself, I don't have any pressure. I'm very confident now."
Red Group play continues Tuesday with number one Andy Roddick opening his account against Spain's Carlos Moya.
Photograph: Getty Images
