Amorim made three changes from the side that beat Leicester City before the FIFA break, as Jonny Evans, Christian Eriksen and Alejandro Garnacho, who joined Bruno Fernandes and Marcus Rashford in attack, were recalled.
United could not make a better start after Rashford sent them ahead inside the first two minutes with a tap-in at the near post after a cross by Amad Diallo.
Ipswich almost responded 10 minutes later when Sammie Szmodics hit a shot that forced goalkeeper Andre Onana to make a save in the bottom corner.
As the game progressed from end to end, Liam Delap could have equalised just before the break after having a fantastic chance with a goal at his disposal but was stopped by Onana.
However, Omari Hutchinson eventually levelled matters for The Tractor Boys on the stroke of half-time with a strike on the edge of the box that took a nasty deflection and flew into the top corner.
The game continued to produce fireworks from the interval with goal-mouth action on either side.
With 22 minutes to go, Amorim went for fresh legs in attack as Rasmus Hojlund and Joshua Zirkzee both came on for Rashford and Christian Eriksen.
It was still anybody’s game as moments later Delap almost gave the home side the lead with a strike from range that missed narrowly wide of the far post.
United had a chance ten minutes before time to restore their lead from a set-piece, as Fernandes came close with a dipping effort that whistled just wide of the far post.
However, chances were few and far between in the dying minutes, with The Red Devils pressurizing The Tractor Boys and the game ended all square.
The result leaves United in 12th place with 16 points, six off the top four. Ipswich are 18th with nine.