Danny Collins' saw his first goals for Ipswich cancelled out at the City Ground.
Collins struck early on before Robbie Findley pegged the Tractor Boys back before the break.
The former Sunderland centre-half grabbed an unlikely second to set up what had appeared to be a convincing win.
But Joel Lynch and Tudgay shocked the travelling fans with headed goals in the last 10 minutes.
Ipswich arrived in Nottingham eager to avoid a fourth consecutive league defeat, and were boosted by the return to fitness of veteran midfielder Lee Bowyer and much-travelled striker Nathan Ellington.
Steve Cotterill, in the hunt for a fifth league win since succeeding Steve McClaren, opted to restore Paul Anderson to the bench after a lengthy absence from first-team action.
Both sides appeared reluctant to start with any conviction.
It was not until the 16th minute that either team registered a shot on target, Guy Moussi's twisting drive collected comfortably by David Stockdale.
Lewis McGugan then took aim from distance but screwed his effort wildly over Stockdale's crossbar.
Perhaps against the run of play, the Tractor Boys seized the advantage with 25 minutes played.
On-loan defender Collins rose to meet Aaron Cresswell's inswinging cross to register his first goal for the Suffolk side.
Cotterill's Reds pressed on regardless in front of the home faithful, and were soon rewarded for their early promise thanks to Findley.
Jason Scotland conceded a free-kick in a dangerous position outside the penalty area, only for McGugan to pick out the American hitman who gleefully tucked home his fifth goal of the season.
After the interval, Collins proved his defensive worth to Paul Jewell by bravely blocking a stinging strike from Moussi, but the Stoke man's impact was soon felt again at the sharp end.
Collins, before today without a league goal since leaving Sunderland two years ago, leapt to glance Jimmy Bullard's corner beyond Lee Camp's grasp and complete a brace on the hour mark.
Summer recruit Jay Emmanuel-Thomas was introduced as Bowyer's replacement and soon gave Camp further food for thought with a left-footed drive, the ball sailing just over the crossbar.
The Reds were to snatch their unlikely victory in a frantic final 10 minutes.
Seven minutes from time, Andy Reid bustled up the left wing to supply Lynch with a tidy cross, the ex-Brighton man nodding home a valuable first goal for the club.
And Tudgay broke the Tractor Boys hearts in the first minute of stoppage time as Greg Cunningham lofted in an accurate pass which the former Sheffield Wednesday frontman nodded home.