Scrumhalf Greg Laidlaw converted all three and added a penalty for the tourists, who were guilty of wasting several other chances to score in the Texas sunshine.
"Was very pleased to see the opportunities created and we will be working next on how we can get over the line and score more points," New Zealander Cotter, who joined from French club Clermont Avergne, told reporters.
The Scots will next face Canada in Toronto on Saturday with the north Americans hoping to pick themselves up after a disappointing second-half collapse against Japan in their Pacific Nations Cup opener.
The Canadians led the Brave Blossoms 25-9 at the break in British Columbia but the Asian Five Nations champions roared back with three second-half tries to claim a 34-25 win.
Japan will face the U.S. next week in California and can claim the Asia Pacific Conference with a record extending ninth consecutive victory.
In the Pacific Islands conference of the tier two tournament, Samoa and Tonga played out an 18-18 draw in Apia on Saturday.
Fiji, who begin the defence of the title at home to Tonga next week, claimed a morale boosting 25-14 win over Six Nations side Italy in Suva on Saturday.
(Writing by Patrick Johnston; editing by Sudipto Ganguly)
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