United had already had a number of chances when Josh Wright crashed a shot into the top corner after 19 minutes, sending the record crowd of 9,077 into raptures.
But it took only four minutes for Darron Gibson to level with a sublime lob and Chris Smalling gave the visitors an undeserved lead at the break.
Within nine minutes of the start of the second half, the result was settled, with Michael Owen scoring a breakaway goal and Park Ji-sung clinically tucking away the fourth.
Owen tapped in his second and United's fifth but the excellent Martyn Woolford at least ensured Scunthorpe had the last say with an injury-time strike.
Phelan said: "I thought Scunthorpe played their part in a very, very good game. They created plenty of opportunities, even when we managed to get it to 5-1 I think we'd had about six chances.
"Overall it's a great scoreline from our point of view because it was a new team out there put together in a couple of days, and Scunthorpe should take a lot of pride and credit from the game."