Johnson completed 21 of 41 passes for 322 yards and Nwachukwu also ran for a score for A&M (2-0), which lost sophomore receiver Jeff Fuller and freshman running back Christine Michael to leg injuries. Fuller was coming off a career-best, 10-catch performance in the season opener against New Mexico and Michael rushed for 94 yards on Saturday before he was hurt.
Diondre Borel threw for 334 yards with a touchdown and also ran for two scores for Utah State (0-2), which has lost eight straight road games and its last 10 games against Big 12 opponents.
A&M's defense played better in the second half after struggling in the first.
On Utah State's initial drive, Robert Turbin burst through a hole and outran A&M cornerback Dustin Harris for a touchdown. Turbin rushed for 121 yards in the game.
Utah State started its second possession near midfield, but Michael Smith fumbled a handoff from Borel and A&M recovered.
Five plays later, Johnson threw a 35-yard pass to Nwachukwu in the corner of the end zone. Officials reviewed the play and confirmed that Nwachukwu's foot landed just inside the orange pylon.
Turbin caught a 20-yard pass from Borel on Utah State's next possession and Borel finished the drive with a 1-yard TD run to give the visitors a 14-7 lead.
A&M gave up 117 rushing yards in the first quarter after allowing only 21 in its 41-6 win over New Mexico two weeks ago.
Nwachukwu tied it again with a 39-yard touchdown sprint, taking a pitch from Johnson and outrunning the defense down the sideline.
Fuller appeared to twist his left knee making a 15-yard reception in the open field early in the second quarter. Two trainers helped Fuller to the sideline and he rode a golf cart to the locker room.
Randy Bullock kicked a 31-yard field goal at the end of the drive to put A&M ahead 17-14.
Harris returned a punt across midfield late in the second quarter. He was hit out of bounds by a Utah State defender and the penalty gave A&M a first down at the 16-yard line.
Nwachukwu then made a diving catch in the end zone near the sideline and a referee on the spot ruled that he was out of bounds. But officials looked at the replay and decided that Nwachukwu's feet touched inside the line.
Chris Ulinski kicked a 42-yard field goal 90 seconds into the second half to cut A&M's lead to 24-17.
A&M quickly moved to midfield and Johnson found Nwachukwu wide open behind the defense for a 50-yard touchdown with 12:20 left in the third quarter. Nwachukwu tied the school record for TD catches in a game.
Michael was injured late in the third quarter when he tumbled forward on a run to the Utah State 18. Trainers helped him off the field, and he spent the rest of the game sitting on a sideline bench.
Johnson threw a 10-yard touchdown pass to Ryan Tannehill early in the fourth quarter.
Borel threw a TD pass to Omar Sawyer and ran for another score in the final six minutes.