NEEDHAM – Aidan Williams needed just one big run to kickstart Needham’s offense.

Once he did, the Rockets never looked back.

Williams rushed for three touchdowns and 143 yards, and the No. 4 Rockets beat the No. 5 Central Catholic Raiders 31-7 in the Division 1 state football quarterfinals Friday at Memorial Field.

Needham (10-0), in the Final Four for the second consecutive year, will take on No. 1 St. John’s Prep, a 44-7 quarterfinal winner over Methuen, in the semifinals next week.

Williams has now scored eight touchdowns in Needham’s first two playoff games.

“I keep calling him the Unicorn,” Needham coach Doug Kopsco said of Williams. “I don’t understand how a dude like this exists. I honestly think he might be the best player in Massachusetts right now.”

Central Catholic (6-4) struck first night when Drew Alsup ran in a 5-yard touchdown with 9:11 left in the second quarter, but the 7-0 lead didn’t last long. Williams broke off a 52-yard run on Needham’s next offensive play, and soon after ran in the 6-yard touchdown to tie the game after Alex Rufo’s first of four extra points.

“I’m just glad that they trust me to run behind this great offensive line that we have,” Williams said. “It’s really the guys up front doing all the work. I just have to read the holes.”

Rufo gave his team the 10-7 lead with a 35-yard field goal with five seconds left in the halftime. The Rockets then started the third quarter with a 12-play drive that took almost eight minutes off the clock.

Griffin Carr twice connected with Joe Kajunski (6 receptions, 105 yards) on big passes to keep that drive alive, including a 56-yard catch-and-run on third-and-26 from the Needham 13-yard line. Rufo also played his part in the drive when a botched snap on a field goal attempt forced Brandt Bickford to try to run for the conversion.

Rufo, a former soccer player trying varsity football for the first time this year, got ahead of Bickford and threw a block to enable the fourth-down conversion. Williams capped the drive with his second touchdown for a 17-7 lead with 4:36 left in the third.

“That was just supposed to be a field goal,” Rufo said. “I heard him (Bickford) behind me go, ‘Just run and block.’ So I started running, and I just hit the first guy I saw.”

That’d be more than enough for the Needham defense, which limited the Raiders to just 87 total offensive yards. Linebacker Alex Rutley brought down Caden Smith on fourth down to end a Raiders drive at their 25, and two plays later Williams ran in his third score with 7:36 left in the game.

Ben Schreiber then capped the defensive effort two plays later when he intercepted Smith and returned it 30 yards to the end zone.

“This might be the defense that we’ve had at Needham High School,” Kopsco said. “They are just relentless. They hunt like a pack of dogs, and it’s very hard for quarterbacks, once they know they have to throw the ball, to get away from that rush.”