The Spurs triumphed despite having to play without guard Manu Ginobili and forward Tiago Splitter, each of whom is expected to miss two weeks due to injuries.
Richard Jefferson's 3-pointer in the final minute sealed San Antonio's longest winning streak since November 2010.
Al Jefferson paced the Jazz with 20 points and 11 rebounds.
Paul Millsap had 16 points and 11 boards as Utah fell to 3-9 in its last 12 games.
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