The Orange (3-5, 1-3 Atlantic Coast Conference) led the Tigers well into the third quarter before falling 16-6 in their first trip to a near sold-out Death Valley.
Syracuse was limited to 170 yards of offense by Clemson's defense, which came in ranked fifth nationally.
Shafer said he was proud of how his players stayed strong in a difficult environment. Still, he understood it's his job to win games and thrive in all situations.
''I apologize to the Syracuse faithful because we're going to get this thing right and we're going to beat these teams eventually,'' said Shafer, in his second season at Syracuse. ''We're just a little bit away right now, but we're going to get this thing right.''
They almost did against the Tigers, who struggled for a third consecutive game to put up points behind backup quarterback Cole Stoudt. The Orange intercepted Stoudt twice and forced a pair of fumbles, an unexpected pile of turnovers from a Tiger team that had only six of them through seven games.
Clemson took the lead for good on Ammon Lakip's third field goal - a 41-yarder in the third quarter. Cole Stoudt threw a 19-yard TD pass to tight end Stanton Seckinger. Then the Tigers put the game away, holding the ball for the final 8:17 to close out a 5-0 October after their first 1-2 start in 10 years.
''We keep finding ways,'' Clemson coach Dabo Swinney said. ''This is a battle-tested group. They're tough minded.''
Stoudt finished for 24 of 35 for 209 yards. He also had three of Clemson's four turnovers with two interceptions and a fumble.
''Hey, a win's a win,'' Stoudt said. ''There were some mistakes here and there, especially in the first half. In the locker room, we got challenged and we came out in the second half and made some plays.''
Stoudt was starting a second straight game for injured quarterback Deshaun Watson.
Lakip had kicks of 38, 18 and 41 yards.
Wayne Gallman finished with 101 yards, the first time a running back has cracked the 100-yard mark this season for the Tigers.
Stoudt hung tough in a Clemson victory for the second straight time after trailing in the second half. A week ago, Boston College led 13-10 before Stoudt led a touchdown drive for the 17-13 win.
This time, he fought through a difficult three quarters before finally finding his footing. After Clemson moved in front on Lakip's final kick, Stoudt had a 17-yard pass to Mike Williams that move the Tigers to Syracuse 23. Two plays later, he found Seckinger.
Clemson iced the game with a final drive that lasted more than eight minutes to run out the clock.
''Mistakes happen. That's football,'' he said. ''I have a mentality of `Hey, let's go on to the next play.' You can't really do anything about the past.''
Syracuse freshman AJ Long, making his second career start, was sacked four times and held to 82 yards passing. Prince-Tyson Gulley ran for 80 yards, accounting for most of the rest of Syracuse's offense.
Syracuse has lost five of its past six games.
''I liked our toughness and resiliency throughout the course of a very difficult, physical football game,'' Shafer said.
This time, though, Clemson's offense continued its freefall without injured quarterback starter Watson. The Tigers, who averaged better than 500 yards a game, the previous two seasons, managed just 157 in the opening half and gave the ball away with two fumbles and an interception.
Two of the turnovers led to Syracuse points.
Clemson got the ball back one final time with 1:22 left when linebacker Dyshawn Davis stripped Stoudt of the ball on the Tigers 22. While Clemson's defense pushed the Orange back, Murphy added a career-long 50-yard field goal - Syracuse's longest kick in six years - for a 6-3 halftime lead.
The Tigers have only one less productive half, points-wise, in offensive coordinator Chad Morris' four seasons than they did against Syracuse - when they were shutout the second half of a 45-21 loss at Georgia on Aug. 30.
''This is a group that could use a week off,'' said Chad Morris, Clemson's offensive coordinator.
The Tigers have next week free before facing Wake Forest on Nov. 6