Murphy had touchdown runs of 47 and 27 yards and finished 12 of 19 passing for 101 yards for the Eagles (4-2, 1-1).
They never trailed and endured a weather delay of nearly an hour to beat N.C. State for the second straight year.
BC, which entered with the ACC's best ground game, outrushed the Wolfpack 310-43.
N.C. State (4-3, 0-3) lost its third straight.
Tony Creecy added a 2-yard scoring run for the Wolfpack. In the second half, they crossed midfield only once, managed just 56 total yards and didn't advance deeper than the BC 39.
The Eagles put this one away with a 10-play, 75-yard drive that chewed up 5:42 of critical time midway through the fourth quarter. Nine plays were rushes - including Murphy's keeper through the right side for the touchdown that iced it with 5 minutes to play.
That BC ran seemingly at will was no surprise: Last year, the Eagles rolled up 420 yards rushing against them - including an ACC-record 339 by Andre Williams.
N.C. State's last ACC victory came in BC's last visit to Raleigh - a 27-10 win in the 2012 regular-season finale.
The Wolfpack were 0-8 in league play during coach Dave Doeren's first season and opened the conference schedule this year with losses to Florida State and Clemson - the latter a 41-0 embarrassment when they finished with just 156 total yards.
Play was stopped in this one for 56 minutes due to lightning and thunderstorms in the Raleigh area - with the suspension coming immediately after BC defensive lineman Brian Mihalik intercepted Brissett's ill-advised pass on the second play of the second half.
Once play resumed on a slick, wet field, the Eagles went nowhere. Mike Knoll's 28-yard field goal gave BC its largest lead to that point, 24-14.
For a while early in this one - when conditions were sunny and dry - defense was merely a rumor, with the teams combining to score touchdowns on the first five possessions of the game.
The most picturesque of those scores belonged to Murphy - who took a keeper around right end for a long TD that briefly gave the Eagles a 14-7 lead.
After Brissett tied it with his scoring pass to Grinnage, Alston took his long end around to the end zone to make it 21-14 roughly 2 1/2 minutes into the second quarter.
Then, the defenses showed up.
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