Stoudt finished 27 of 42 for 282 yards with three touchdowns -- two to Scott, one to Wayne Gallman -- and Gallman added a late rushing score to help the Tigers (7-2, 6-1 Atlantic Coast Conference, No. 21 CFP) win their sixth straight.
John Wolford was 11 of 29 with two touchdown passes to Cam Serigne, covering 4 and 14 yards, for Wake Forest (2-7, 0-5).
Mike Weaver tied it twice with field goals, including a 31-yarder that made it 20-all with 11:08 left.
On Clemson's next play, Scott came in motion while Stoudt took the snap and tapped it forward. The freshman caught it and weaved through the right side and into the end zone.
Clemson's No. 2-ranked defense forced a three-and-out and Gallman made it a two-score game for the first time with his touchdown run with 6:36 left.
The Tigers outgained Wake Forest 427-119. The Demon Deacons, who have the worst rushing offense in the Bowl Subdivision, managed just 7 yards on the ground -- Wolford was sacked five times -- while losing their fifth in a row.
Gallman rushed for 106 yards, and Scott had 122 yards receiving.
Stoudt went the distance under center for the Tigers while injured freshman Deshaun Watson sat out his third straight game with a broken bone in his throwing hand.
Watson was in uniform and spent most of the night wearing an earpiece after coach Dabo Swinney said earlier in the week that he could play but probably wouldn't unless Clemson needed him.
For much of the night, it seemed like the Tigers might need him.
Clemson, a three-touchdown favorite, had beaten Wake Forest by at least 20 points four times since 2008 but at no point did this one seem nearly that easy.
The Demon Deacons, donning shiny new gold-chrome helmets, kept things interesting during a disjointed game in which each team essentially gifted a touchdown to the other one with a special-teams miscue.
The first half ended on hands-to-the-face penalty on Clemson on the final snap gave Wake Forest a free play that the Demon Deacons turned into Weaver's career-long 50-yard field goal that tied it at 17.
Wolford's first touchdown pass to Serigne, covering 4 yards, came four plays after the quarterback caught a 24-yard pass on a trick play. Those two hooked up again from 14 yards out after Clemson's Matt Humphries muffed a wind-blown punt deep inside Tiger territory.
Two of Stoudt's TD passes came before halftime, with his 18-yarder to Gallman coming after Wake Forest punter Alex Kinal fielded a long snap with his knee on the turf at his own 23. His first score to Scott covered 4 yards, came with 27 seconds before the break and gave the Tigers a 17-14 lead that disappeared after Tavaris Barnes' untimely personal-foul flag.
Ammon Lakip kicked two field goals, including a 39-yarder into a stiff wind on the opening drive of the second half to give Clemson a 20-17 lead.
Tigers pull away late
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