The Spurs suffered their first setback in Space City on Thursday, falling to Houston 105-85. DeJuan Blair led San Antonio in that one with 22 points and 12 rebounds, while Tony Parker added 12 points and Tiago Splitter donated 10 points and 11 rebounds off the bench.
The Spurs had won their first two contests, over Memphis on Monday and the Los Angeles Clippers on Wednesday.
"We just mentally were not here," Ginobili said. "They played a terrific game."
The Jazz, meanwhile, recorded their first win on Friday, a 102-99 triumph over Philadelphia in Salt Lake City.
Paul Millsap also recorded a double-double with 14 points and 14 boards for the Jazz, who avoided their first 0-3 start since opening the 1979-80 season with four straight losses. Devin Harris added 19 points, Gordon Hayward had 15 and C.J. Miles had 10 in the win.
"We needed a win, first of all," Jazz head coach Tyrone Corbin said. "We made some mistakes tonight, but I thought our energy level was up and defensively I thought we did a great job communicating with each other. The guys did a good job of coming together and pushing each other."
Jefferson, who was a late scratch Friday with an injured right ankle, is questionable for tonight's contest.
These two clubs have traded season sweeps over the past three years. San Antonio won all three meetings over the Jazz in 2010-11 and took four straight back in '08-09 but Utah swept four over the Spurs in '09-10.