Florida Atlantic (2-6) trailed 38-0 before quarterback Jaquez Johnson scored on a 29-yard run with less than 1 minute remaining in the first half.
Jeremy Johnson completed 10 of 16 passes for 192 yards with two touchdowns and one interception.
Auburn, which leads the SEC and ranks No. 8 in the nation in rushing offense, had 422 yards rushing. Cameron Artis-Payne led the Tigers with 93 yards rushing, including a 1-yard scoring run in the third quarter.
Big plays on offense, defense and special teams helped Auburn build a big early lead.
Marshall had a 46-yard run to set up Tre Mason's 8-yard touchdown run on Auburn's first possession.
On the Owls' fourth play, running back Jonathan Wallace's fumble was recovered by Jermaine Whitehead. The turnover, forced by defensive end Dee Ford, set up Corey Grant's 43-yard touchdown run one play later to give Auburn a 14-0 lead less than 4 minutes into the game.
Auburn's special teams added a big play in the first quarter. Chris Davis returned a punt from near the Auburn goal line 70 yards to the Florida Atlantic 28. Marshall scored on a 10-yard run four plays later.
Marshall hurt his shoulder when sacked by defensive end Eugene Robinson on the second play of the second quarter. Auburn reported Marshall was held out for precautionary reasons.
The sack left Auburn with a third-and-13 play from the Florida Atlantic 36. Jeremy Johnson took the shotgun snap and passed to Coates, who was open on the Owls' sideline.
Later in the second quarter, Coates got behind the Florida Atlantic defense in the middle of the field and, without breaking his stride, caught Johnson's deep pass for the 67-yard touchdown. Owls cornerback Cre'von LeBlanc fell after his unsuccessful diving attempt at the ball.
Jaquez Johnson completed 9 of 20 passes for 133 yards as the Owls were held to 247 total yards. He led Florida Atlantic with 58 yards rushing.
Florida Atlantic linebacker Freedom Whitfield was taken to a local hospital after he was injured on a collision in the first quarter.
Whitfield led with his helmet on a big hit against Davis. Whitfield's helmet appeared to hit Davis high on his chest. Part of Whitfield's helmet may have hit the lower facemask of Davis.
Both players initially were stunned following the collision, but Davis rose while Whitfield remained on his back.
Whitfield, who was strapped to a stretcher, moved his left arm in response to teammates who approached him as he was taken off the field on a cart.
There was no immediate update on Whitfield's condition.