They also were feeling some pain.
''I'm sore,'' said reserve Stephen Jackson, who played 26 minutes in the down-to-the wire 87-81 victory. ''Those guys play hard.''
Fortunately, the Spurs are going to get some rest before the next round.
San Antonio awaits the winner of the Grizzlies-Clippers series, which may not be decided until Sunday. The Clippers lead 3-1 after winning 101-97 in overtime on Monday night.
''There's going to be some rust there,'' All-Star Tim Duncan said of the wait between series. ''We have been playing so many games back to back, you're going to lose your rhythm a little. ... But health-wise and for us to get 100 percent in the tank, it's great.''
The Spurs blew out the Jazz by 58 points combined in the first three games but had to sustain a furious rally Monday after going up by as many as 21 points in the fourth quarter.
''This is probably the hardest-playing team in the league,'' said Jackson, who was part of the Spurs bench that contributed 57 points. ''The way they played the last five minutes showed the character of this team. We take our hats off to them. They fought to the end.''
The Spurs can thank their bench for keeping them in it.
Star sixth man Manu Ginobili hit consecutive 3-pointers after the Jazz had pulled within 61-58 late in the third quarter. And after the Jazz rallied from 21 down to get within four on Al Jefferson's put-back in the final minute, Ginobili turned a steal by MVP candidate Tony Parker into a layup that sealed the win.
''I wasn't making many shots, but I wasn't taking that many either,'' said Ginobili, who was 0 for 8 from 3-point range in the first three games but had three 3s Monday and finished with a team-high 17 points. ''I really wasn't that worried. I was happy that the team was playing as well as we were. We were 3-0 and winning those games with authority.''
It was the West's second first-round sweep as Oklahoma City eliminated defending champion Dallas in four games.
The Spurs won Game 1 by 15 points, Game 2 by 31 and Game 3 by 12, relying on Parker, Duncan, key young players and the deepest bench in the league.
Parker had 11 points on 4-of-14 shooting Monday, Duncan added 11 points on 4-of-10 shooting, and starters Kawhi Leonard, Boris Diaw and Danny Green combined for a total of eight points. The Spurs' bench picked up the slack, outscoring Utah's reserves 57-10 and finishing with 27 more points than their own starters.
''We've been a deeper team this year than we usually are and it sure came in handy tonight,'' Popovich said.
Facing elimination, the Jazz started their Big 3 lineup, with Derrick Favors at power forward, Jefferson at center and Paul Millsap moving to small forward.
After a slow start, they made a difference, with Favors registering impressive blocks on Parker and Tiago Splitter and dominating the boards. The trio combined for 52 points, 39 rebounds and five blocks.
It was the first game of the series that Utah held an advantage in the paint (34-30).
And the Spurs were feeling it afterward.
''It's good to get this series over with and not have to worry about these guys because they're definitely a hard team to play against,'' Jackson said.
Now it's either Memphis, which knocked the Spurs out in the first round last year, or the Chris Paul-led Clippers.
''We're gonna watch it,'' Jackson said of the Grizzlies-Clippers series. ''We watch all the games. We'll just continue to stay focused and be prepared so when the series is over, we're ready to go. It's a tough series either way. Both are good teams.''
The Spurs are seeking their fifth NBA title. Yet Ginobili said no one was looking that far ahead.
''Our defense is good and our offense is getting better slowly,'' he said. ''We are just going to stay humble and focus on our next opponent and not on the Finals yet.''
- San Antonio Spurs