The Lions were unbeaten in 22 games at The Den until Saturday's shock 6-1 mauling by Watford.
And a second home defeat was hot on its heels as Roy Keane's Ipswich condemned them to back-to-back losses on their own turf for the first time in 18 months.
Hungarian frontman Priskin struck his third goal of the season in the 23rd minute and defender McAuley doubled the lead before the break.
Steve Morison pulled one back in the second half but Ipswich held off a late onslaught to reach the fourth round for the first time in eight years.
While Keane made eight changes to his side, who are flying high in the npower Championship, Lions chief Kenny Jackett gave eight of the players responsible for their weekend humbling a chance to make amends.
They should have had the perfect tonic after just four minutes when James Henry's cross found Morison all alone on the six-yard line but the striker headed wide.
Ipswich goalkeeper Brian Murphy kept out another Morison effort and also denied overlapping full-back and former Tractor Boy Scott Barron in the opening quarter of an hour.
Ipswich then went ahead with their first attack of note, Tottenham loanee Andros Townsend crossing for Priskin to loop a header over David Forde and into the net.
Townsend almost made it 2-0 in spectacular fashion but his angled 25-yard drive flew narrowly wide.
But the lively Spurs teenager had a hand in the second goal, on the stroke of half-time, when his low free-kick was helped past Forde by the outstretched leg of McAuley.
The Den faithful are not renowned for their sympathy when things are going against their team, and their mood did not improve early in the second half when Alan Dunne crossed to Chris Hackett only for the winger to miss his shot in front of goal.
They were given something to cheer in the 62nd minute when Morison halved the deficit in fine style, controlling Tony Craig's high cross and turning in an instant to hit his sixth goal of the season.
The Lions poured forward late on and Morison headed over before Liam Trotter's shot flew too high, but they could not find a way through as Ipswich held on.