Rashford also scored a quick goal in Ole Gunnar Solskjaer's first game, netting three minutes in at Cardiff after the Norwegian had replaced Jose Mourinho in December 2018.
This effort was even quicker and must have been satisfying for Amorim given he had trusted Amad with the right wing-back berth in his new formation and picked Rashford ahead of Rasmus Hojlund and Joshua Zirkzee in the key central striking berth.
The visitors did have other opportunities. Alejandro Garnacho curled an effort narrowly wide and Diogo Dalot darted into the penalty area to meet Casemiro's angled pass.
Unlike in the West Ham defeat that triggered Ten Hag's dismissal, when he blazed over from a similar position with the goal at his mercy, this time Dalot kept his shot on target. But it lacked the power to test Arijanet Muric.
But it was not a smooth United performance by any means and Onana had arguably been the visitors' key man even before Ipswich equalised.
The Cameroon international's first save to deny Delap was stunning. Leif Davis waited until just the right moment before playing the pass to Delap, who only had the United goalkeeper to beat.
Onana didn't just stop the shot. He also had enough power to push the ball away to safety rather than present Ipswich with a rebound.
His second-half save was just as important as Delap got to Wes Burns' low cross first and flicked the ball towards goal with the back of his foot from barely two yards. Onana's reactions were up to the task.
In attack, United were lightweight. Garnacho sprinted into the penalty area but looked as though he was trying to play a square pass to Rashford before Jens Cajuste slid in to rob the Argentine.
Amorim tried to shake things up with a series of second-half substitutions but other than Fernandes' free-kick, his side did not threaten.