The Swifts were without ten players for the trip to Solitude as they hit a spanner in the works for Cliftonville's title dreams.
The hosts were looking good for all three points when Ronan Hale headed in the opener just before the hour mark.
However, the Swifts would produce a stunning fightback as Padraig Lynch equalised with 90 minutes on the clock, before Joe Moore slammed home an injury time winner soon after to make it two wins for Dungannon at Solitude in a matter of weeks.
"I think it's one of the best results in the club's history for the past couple of decades because of the circumstances," Shiels told Dungannon Swifts TV.
"We had ten players out - seven of those with an illness.
"We tried to get the game called off and we approached the League twice on Friday.
"There were players playing half-cocked, not fit and out of position.
"To come and win here is a magnificent effort and I'm really proud of the group.
"We had to pull seven players from the U20's and that shows what the club is all about.
"The Under-20 players came on and gave us a big lift, energy and quality at the same time.
"I'm really proud of the whole group."
The Swifts knocked Cliftonville out of the Irish Cup at the same venue a fortnight ago and Shiels argued he would rather have had the Premiership points than the Irish Cup scalp if offered before a ball was kicked.
He was also full of praise for the young talent of players coming through the conveyor belt at Stangmore Park.
"I think it's hard to enjoy games and hard to enjoy moments when the club's survival is at risk," he added.
"The Irish Cup is superb and it's really good to be in the semi-final but I know deep down, I'd have taken three points in the League game instead.
"Thankfully, we were able to come here and do the same.
"We have got so many young players who are nearly on the cusp of it.
"We try and promote them as much as we can but the issue is that you're throwing them all in at once.
"You try to dip feed them and manage their minutes, as well as being in a relegation fight, so it's hard to develop players.
"It's hard to play out from the back and have the playing style we have when you're fighting relegation but that takes bravery, guts and belief.
"The young players coming through are being taught the same as the first-team and when they come on, they know their roles and it all comes together.”
CLIFTONVILLE: Gartside, Addis (C. Curran '46 mins), Gallagher (Gormley '57 mins), Rory Hale, R. Curran, Lowe, R. Doherty, Turner, Ronan Hale, Coates (Parkhouse '90 mins), Moore (Rocks '75 mins).
Subs Not Used: Donnelly (GK), McDonagh, Robinson.
DUNGANNON SWIFTS: Dunne, Marron, Knowles, O'Connor (Lynch '81 mins), Curry, McGinty, Walsh (Cushnie '67 mins), Jenkins (Smith '81 mins), Animasahun, Scott, Bruna (Moore '67 mins).
Subs Not Used: Nelson (GK), Francis, Donnelly.
Referee: Helgi Mikael Jonasson2023-03-19T13:20:56Z dg43tfdfdgfd