Broughton rushed for 124 yards and a touchdown, while Hooks had 77 yards and a score himself.
Last week, neither the Tigers (1-1) nor the Rattlers (1-1) could mount much offense and it continued this week, though Tennessee State found just enough.
The Tigers benefited more from their special teams and defense than their offense.
In the first quarter for example, FAMU quarterback Damien Fleming changed the play at the line of scrimmage, fooling no one. Tigers safety David Van Dyke jumped the new route, picked off Fleming and returned the ball 46 to give TSU a 7-0 lead.
Later in the quarter, Broughton's 10-yard scoring run gave Tennessee State its first offensive touchdown for the season.
Florida A&M finally got on the board when Fleming connected with Lenworth Lennon from 36 yards out to cut the Rattlers' deficit to 14-7 in the second quarter.
That momentum evaporated 14 seconds later, however. On the ensuing kickoff, Martine Stevenson, a redshirt junior, cut right through the middle of FAMU's special teams and raced 95 yards for the touchdown. It was TSU's first kickoff return for a touchdown since Weldon Garlington did it Oct. 1, 2011 against Austin Peay.
Hooks scored from 14 yards out in the third quarter to complete the scoring.
The Aggies (1-0) scored 24 straight points and withstood a furious fourth-quarter rally from the Mountaineers (0-2) at Kidd Brewer Stadium in Boone.
ASU took the early lead when Jamal Londry-Jackson hit Marcus Cox for a 35-yard score in the first quarter.
NC A&T answered back quickly when Tony McRae took the ensuing kickoff back 91 yards for a 7-6 lead.
As time ran out in the first quarter, signal caller Kwashaun Quick found Desmond Lawrence for a two-yard scoring toss.
D'Vonte Grant's 57-yard interception return of a Londry-Jackson pass made it 21-6 heading into halftime.
The Aggies closed out their scoring in the fourth quarter on Cody Jones' 27-yard field goal.
Appalachian State had switched out quarterbacks at halftime, substituting Kameron Bryant for Londry-Jackson and the move paid off in the fourth quarter.
Bryant threw for 191 yards and connected with Barrett Burns and then Cox for touchdowns. Unfortunately, Cox's score came with 24 seconds left in the game.
Jackson State 30, Alabama State 23
Bethune-Cookman 66, Virginia Union (D-II) 7
(4) Clemson 52, South Carolina State 13
Delaware 42, Delaware State 21
Delta State (D-II) 24, Mississippi Valley State 14
Howard 27, Morehouse (D-II) 16
Louisiana-Monroe 48, Grambling State 10
McNeese State 58, Arkansas-Pine Bluff 14
Mississippi State 51, Alcorn State 7
North Carolina A&T 24, Appalachian State 21
North Carolina Central 23, St. Augustine's 20 (D-II) (2OT)
Northwestern State 55, Southern 14
Robert Morris 31, Morgan State 13
Rutgers 38, Norfolk State 0
Tennessee State 27, Florida A&M 7
Texas State 28, Prairie View A&M 3
Troy 66, Savannah State 3
Tuskegee (D-II) 23, Alabama A&M 7
Johnson C. Smith 34, Livingstone 17
Virginia State 29, Fayetteville State 28
Benedict 42, Central State 9
Bethune-Cookman (FCS) 66, Virginia Union 7
Bowie State 42, St. Anselm 28
Howard (FCS) 27, Morehouse 16
Johnson C. Smith 34, Livingstone 17
Lane 38, Virginia-Lynburg 13
Lincoln (Pa.) 33, Cheyney 28
Lock Haven 31, West Virginia State 13
Newberry 35, Elizabeth City State 32
N.C. Central (FCS) 23, St. Augustine's 20 (2OT)
North Greenville 26, Albany State 24
Shaw 44, College of Charleston 14
Stillman 52, Concordia-Selma (NAIA) 0
Tuskegee 23, Alabama A&M (FCS) 7
UNC-Charlotte 47, Chowan 7
UNC-Pembroke 25, (5) Winston-Salem State 21
(1) Valdosta State 36, Fort Valley State 21
(13) West Alabama 42, Clark Atlanta 6
Avila (Mo.) 80, Haskell Indian Nation 13
Incarnate Word 69 (D-II), Texas College 0
Northwestern Iowa 55, Bacone 37
Stillman (D-II) 52, Concordia-Selma 0