The Tigers also recovered from a 10-point fourth-quarter deficit to go ahead with under two minutes left in the game.
But the Tigers had no answer for Farmington junior quarterback Justin Boehm, which ultimately did them in Friday night.
Boehm put on a spectacular performance, accounting for 434 yards of total offense and throwing the winning touchdown pass with 20 seconds left to cap a wild 39-36 homecoming win.
"I have never been in a game like that before," Central senior Jacob Campbell said.
Boehm said he has never had a game like that even though he has turned in other strong performances this season.
"That's got to be my best game," Boehm said. "We were waiting for a game like that."
The Knights (2-4), among the region's top teams in recent years but struggling this season, broke a three-game losing streak while handing Central (2-4) its third straight defeat.
Central looked like it would overcome an early 20-0 hole, a late 33-23 deficit and what Tigers coach Nathan Norman called a lack of mental focus when Campbell scored his fourth touchdown of the night from his tailback position.
Campbell's 11-yard run with 1:17 left capped a 77-yard, 10-play drive on which the Tigers overcame a second-and-20 hole from deep in their territory.
But Boehm would not let Central escape with a victory. He needed less than a minute to drive the Knights 77 yards in six plays.
Boehm rushed twice for 15 yards and completed two passes for 24 yards, putting the ball at the Central 38-yard line.
A first-down pass fell incomplete. Boehm dropped back on second down and looked for his favorite target, senior wide receiver Evan Dunivan.
Dunivan, much to the surprise of just about everybody in Farmington's stadium, was wide open along the right sideline.
"I was very surprised," said Dunivan, who had 11 receptions for 196 yards.
Boehm lofted a pass that hit Dunivan in stride at about the 10-yard line and he cruised into the end zone.
"I guess they had a lapse in coverage," Boehm said. "I just had to get it to him."
Said Norman: "Just a blown coverage. We told the kid don't bite on anything short. He did."
Farmington's win was complete when the Knights recovered a squibbed kickoff that bounced off a Central player. Boehm took one kneel-down and time expired.
"We knew we had to play all four quarters. Cape is a very good team," Boehm said.
Boehm's numbers were staggering. He rushed for 166 yards on 40 attempts and scored four touchdowns. He completed 18 of 29 passes for 268 yards and a pair of touchdowns, both to Dunivan.
Boehm, listed as 6-feet and 165 pounds, repeatedly burned the Tigers with a mixture of called runs and scrambles when he could not find a receiver or was flushed out of the pocket.
"I give him his props," Campbell said. "He played one hell of a game."
The Tigers could not have had a worse start. They received the opening kickoff but lost a fumble on the game's third play.
Farmington had to drive only 35 yards for a touchdown. Central then lost another fumble on its first play after the TD. This time the Knights marched 51 yards to make it 14-0.
"We weren't mentally there. I fumbled," Campbell said. "We played hard, but mentally we weren't there."
Central's third possession resulted in a three-and-out, followed by a 61-yard Farmington touchdown drive that made it 20-0 late in the opening quarter.
"Obviously we got off to a slow start. We can't do that," Norman said. "You have to be ready to go. I blame myself. I have to get them motivated after a big game [the previous week's 29-26 loss to rival Jackson]."
The Tigers shook off the rough start and seemed to gain control.
Senior tailback Chris Martin's 79-yard touchdown run with 54 seconds left in the first quarter made it 20-7.
Farmington drove inside Central's 10-yard line, but senior defensive back Alex Davis-Carter picked off Boehm in the end zone on fourth down. It was the first of two interceptions by Davis-Carter.
Central drove 88 yards and Campbell scored from 1 yard out to pull the Tigers within 20-13, although the PAT was blocked.
The Knights' next possession resulted in a lost fumble as senior defensive end Jared Thomas made the recovery at Farmington's 34-yard line.
Campbell's 1-yard run, one play after junior quarterback Dennis Vinson hit senior wide receiver Garan Evans on a 33-yard strike, forged a 20-20 tie with 5:28 left before halftime.
Central continued its surge with a 55-yard drive capped by senior Calvin Lovig's 35-yard field goal 27 seconds before the break, sending the Tigers to their locker room ahead 23-20.
"We battled back," Norman said.
Farmington used drives of 66 and 80 yards to surge back on top 33-23 with under eight minutes left in the game.
Campbell's 45-yard touchdown jaunt with 6:15 remaining made it 33-29 -- a pass for two points failed -- and Davis-Carter's second interception, again on fourth down, led to Central's 77-yard drive that put the Tigers ahead.
Boehm and Dunivan then conspired to ruin Central's apparent comeback.
"We fought back, but we were never in the game mentally like we should have been. It cost us," Norman said. "But take nothing away from Farmington."
Campbell rushed for 114 yards on 14 carries. He shouldered much of the ground load after Martin, Central's top rusher on the season, suffered a foot injury midway through the second quarter and did not return.
Martin gained 98 yards on nine attempts before going down.
"We usually share [carries]," Campbell said. "I had to do it for Chris. I had a responsibility."
Farmington had 468 total yards compared to 413 for Central, which rushed for 284 yards.
Vinson completed 7 of 14 passes for 129 yards. Evans had three receptions for 85 yards.
F -- Justin Boehm 3 run (Alec Vanstavern kick), 7:39
F -- Boehm 5 run (Vanstavern kick), 5:57
F -- Evan Dunivan 20 pass from Boehm (kick failed), 1:16
C -- Chris Martin 79 run (Calvin Lovig kick), :54
C -- Jacob Campbell 1 run (kick blocked), 6:08
C -- Campbell 1 run (Lovig kick), 5:28
C -- Lovig 35 FG, :27
F -- Boehm 5 run (kick failed), 3:15
F -- Boehm 3 run (Vanstavern kick), 7:20
C -- Campbell 45 run (pass failed), 6:15
C -- Campbell 11 run (Lovig kick), 1:17
F -- Dunivan 38 pass from Boehm (kick blocked), :20
RUSHING -- Central, Campbell 14-114, Martin 9-98, Mikey Jones 5-61, Dennis Vinson 5-3, Keneen Abraham 2-3, Rene Reyes 1-5. Farmington, Boehm 40-166, Grant Hopkins 9-14, Anthony Greco 3-22, team 1-minus 2.
PASSING -- Central, Vinson 7-14-0-129. Farmington, Boehm 18-29-2-268.
RECEIVING -- Central, Garan Evans 3-85, Kyle Thompson 2-26, Campbell 1-13, Jacob Boerboom 1-5. Farmington, Dunivan 11-196, Greco 3-34, Jared Dunlap 3-18, Hopkins 1-2