The sophomore quarterback threw for a touchdown and ran for another score before leaving early in the third quarter with a strained hip.
X-Rays and MRI results both came back negative, but as of now he's considered questionable to play next Saturday's game at Maryland.
Boyd, who completed 16-of-26 passes for 283 yards, was hurt on Clemson's opening drive of the second half. He was injured when he was hit by a Boston College defender while completing a pass to tight end Dwayne Allen for five yards.
Freshman Cole Stoudt took over for Boyd and finished with 37 yards through the air.
"I saw that Tajh was injured and I wasn't sure what was wrong at the time," Stoudt said. "I just knew I had to step up and do my part. The coaches just told me to relax and have fun. They told me to maintain ball security and stay focused."
Andre Ellington gained 117 yards on 22 carries and scored a touchdown for Clemson (6-0, 3-0 ACC), which jumped out to a 20-0 lead.
Chase Rettig had 129 yards on 13-of-20 passing with one touchdown and one interception for the Eagles (1-5, 0-3).
Clemson got to a fast start as its first three drives produced 17 points in the opening frame.
Jaron Brown hauled in a three-yard TD pass from Boyd, Chandler Catanzaro converted the first of his five field goals, a 38-yarder, and Boyd rushed 14 yards to the end zone. Boyd's TD run was preceded by a Rettig fumble.
After Catanzaro drilled a 42-yarder with 6:58 left in the second quarter, Rolandan Finch scored on a 20-yard run to put Boston College on the board. Catanzaro connected from 18 yards to put Clemson up 23-7 at halftime.
"They got rocketshipped out of there at 17-0 really fast," BC coach Frank Spaziani said. "They have a lot of good players over there, a lot of good playmakers. They made some plays, and we were there to make plays, but we didn't make them...36-14, that's the result."
In the third quarter, Catanzaro sandwiched a 24-yard TD pass from Rettig to Bobby Swigert with a pair of field goals (20 and 47 yards).
Ellington sealed the win in the fourth quarter with a 35-yard TD run on fourth down.
Clemson inched ahead in the all-time series, 10-9-2...Stoudt was 6-of-10 passing...Sammy Watkins had 152 yards on seven receptions for the Tigers...Finch carried 19 times for 81 yards.