The frontman came on midway through the second half, scored twice in quick succession and then clattered the post with a free-kick.
Magilton said: "Jon came on and made a big difference.
"He was particularly disappointed with his performance in midweek (in the 1-1 draw against Charlton). He was very hard on himself.
"But today he came on and scored two great goals and he could have scored a hat-trick.
"Overall, our performance was fantastic and we'd been longing for a clean sheet. We're becoming hard to beat and that's one defeat in 11 games.
"We're showing a great work ethic and the boys showed their mettle.
"We all loving playing on sunny days when the pitch has been manicured, but these were tricky conditions and I thought we adapted very well. The fact we were patient and got our rewards was also very pleasing.
"Now we've got to keep that resolve and belief going."
Stead had been introduced in the 68th minute and wasted no time in breaking the deadlock, nodding over the line after his initial effort had been saved by Radek Cerny.
Then, three minutes later, he powered an unstoppable header into the net after a corner from Owen Garvan.
Town deserved maximum points as they dominated the second period.
Stead could have had a hat-trick but his brilliant free-kick clattered the right-hand post, while Kevin Lisbie's effort when one-on-one was stopped by Cerny.
The best chance before the break had fallen to Rangers, but Martin Rowlands' point-blank header was brilliantly saved by Richard Wright.
Caretaker Rangers boss Gareth Ainsworth said: "Ipswich took their chances after the break whereas we missed ours in the first half - that was the difference.
"Richard Wright made a fantastic save to deny us and then we hit the bar.
"To concede two goals from set-pieces was disappointing but I can't fault the lads' effort. On Tuesday night we played with 10 men for 60 minutes against top-of-the-table Birmingham.
"There were a lot of tired legs out there today and the midweek game took its toll. The boys faded in the second half and that's understandable because of the effort they gave in that game.
"But the commitment was still there, which was a big positive, and we know we can score goals."
Of his own position in temporary charge, Ainsworth added: "We're taking it day by day at the moment."
Sporting Life.