Western Conference top seeds San Antonio, who were stunned by Memphis in last year's playoffs, sealed the best-of-seven series against Utah 4-0 with their 14th consecutive win.
Manu Ginobili scored 17 points while Tony Parker and Tim Duncan played sparingly, finishing with 11 points apiece.
"Last year was frustrating," Ginobili told reporters. ""But like I said many times, last year the Grizzlies played better than us. I think we played better this year."
Utah raised the home crowd's hopes of avoiding the sweep by climbing out of a 21-point deficit midway through the fourth quarter, but San Antonio moved up a gear and put the Jazz away.
While the defeat marked the end of Utah's season, their youthful roster have gained valuable playoff experience. Al Jefferson led them in scoring on Monday with 26 points and 10 rebounds.
San Antonio will next play the Los Angeles Clippers or Memphis Grizzlies in the next round and it is looking likely that it will be the Clippers after they seized a 3-1 lead in their first-round series on Monday.
Chris Paul scored eight of his 27 points after regulation to lead Los Angeles to a thrilling 101-97 overtime win against the Grizzlies.
Game Five is on Wednesday in Memphis.
In Utah, the Jazz shook things up by inserting second-year player Derrick Favors into the lineup. He tallied 16 points and 10 rebounds to help Utah out-rebound the visitors 57-43, but it was far from enough.
Coach of the Year Gregg Popovich was able to guide his team to the best record in the conference this season while still managing to rest his core of veteran standouts.
Popovich continued to manage his players accordingly as his reserves made up the difference with 47 bench points.
"Looking at it from the beginning of the game I thought that our guys showed a lot of class as they have done all year - just continued to fight," said Utah coach Tyrone Corbin. ""Our backs were up against the wall right from the beginning."
