Johnson was 31-of-39 passing and also ran for a touchdown for the Aggies (3-5, 1-3), who set a season high for points and picked up their first Big 12 win under coach Mike Sherman.
The teams racked up 1,083 yards of total offense, converted 23 of 31 third downs and punted just twice in yet another Big 12 offensive show.
But it was Johnson who provided the difference, finding four different Texas A&M receivers for at least six catches. Jamie McCoy led the way with 110 yards receiving and two TDs as Johnson tore up an Iowa State defense ranked 90th in the nation in pass defense entering play.
Austen Arnaud threw for a career-high 371 yards and a touchdown for Iowa State (2-6, 0-4), which dropped its sixth straight and is now the Big 12's only winless team in conference play.
Johnson directed two straight scoring drives after the Cyclones got within 28-20 midway through the third quarter. He got Texas A&M moving late in the third quarter with his longest pass of the night, a 43-yard pass to Jeff Fuller, and Jorvorski Lane's 1-yard TD run put the Aggies back ahead 35-20 heading into the fourth quarter.
Johnson's 5-yard TD run with 11:27 left made it 42-20.
Arnaud pulled the Cyclones within 42-28 on a 9-yard TD run midway through the fourth quarter. Johnson answered by hitting Fuller for an 8-yard score with 4:22 left, only to watch Arnaud throw a TD pass to Collin Franklin 52 seconds later.
Fuller had a team-high eight catches for Texas A&M.
Johnson had 215 yards passing and three touchdowns in the first half and Texas A&M led 28-17 at the break.
Johnson snapped a 14-all tie with a 12-yard TD pass to Jamie McCoy, and Cyrus Gray pushed Texas A&M's lead to 28-14 on a 27-yard touchdown run with 1:22 left in the second quarter.
Alexander Robinson scored from 1 yard out to give the Cyclones a 7-0 lead on the game's first possession. Johnson answered quickly, finding a wide-open Terrance McCoy for a 35-yard TD strike to tie the game at 7 midway through the first quarter.
Johnson then hit Jamie McCoy from 37 yards out to make it 14-7 early in the second quarter. Iowa State tied the game on a 1-yard TD run by Jason Scales.
Texas A&M running back Mike Goodson didn't suit up. Goodson, the Aggies leading rusher with 386 yards and five touchdowns, sprained his knee last week in a loss to Texas Tech.
Johnson fell shy of his single-game best of 419 yards passing, which he did against Kansas State on Oct. 11.
R.J. Sumrall had a game-high 143 yards receiving for Iowa State, which lost despite racking up 574 yards of total offense and zero punts.
Amazingly, this was the fewest points Texas A&M has allowed in conference play.