Courtney Herndon returned a blocked punt for a touchdown for the Wildcats (4-2, 1-1 Big 12), who moved the ball at will in the first half and led 27-10 at the break.
Freeman led a 98-yard drive the other way and sealed the win on a short touchdown run with 4:37 left.
Johnson, starting again for the injured Stephen McGee, completed 29 of 41 passes for a school-record 419 yards. He also ran for a score and finished with 487 total yards, also a school record.
The Aggies (2-4) gave up 451 yards and dropped to 0-2 in the Big 12 for the first time.
The Wildcats found the end zone on their opening drive for the fourth time this season. Freeman threw a 32-yard pass to Brandon Banks before scoring on a 12-yard run just over three minutes into the game.
A&M's first drive stalled at the Kansas State 9 and Randy Bullock kicked a 26-yard field goal.
Kansas State again drove to the Aggies' 12, but Freeman fumbled after a hit by linebacker Von Miller.
The Wildcats glided down the field again on their next possession. Logan Dold finished the drive with a 4-yard TD run. Freeman went 6-for-7 and scampered for 12 yards on a fourth-and-1 from the Aggies 28.
Freeman finished a quick drive with another touchdown run with 4:20 left in the half. At that point, the Wildcats had 269 total yards and were averaging 7.7 yards per play.
Mike Goodson, who sat out the first quarter, broke a 23-yard run on the Aggies' next play. Howard Morrow, who had only one catch this season, made a diving grab on a deep throw at the Kansas State 7.
On fourth down from the 1, Lane barreled into the end zone for his first touchdown of the season. Lane set two school records with his 46th career touchdown and his 45th rushing. He had been tied with Darren Lewis for first on both lists.
Brooks Rossman kicked a 49-yard field goal for Kansas State in the third quarter. Johnson took the Aggies on a 12-play drive over the next five minutes and finished it with a 5-yard touchdown run. Bullock missed the extra-point attempt.
The Aggies drove to the Kansas State 2 early in the fourth quarter, but Lane was gang-tackled on third and fourth down.
After Kansas State's 98-yard drive, Johnson threw a 23-yard touchdown pass to Goodson. The Wildcats recovered the ensuing onside kick near midfield and Freeman scored again with 1:14 left.
Johnson threw a 55-yard touchdown pass to Tannehill in the final minute.