Bursaspor's teenage midfielder Tufan came off the bench with 14 minutes remaining of Wednesday's clash, and he opened his full international account in style with an unstoppable 25-yard drive that arrowed past Kasper Schmeichel.
The 19-year-old's wondergoal completed a remarkable turnaround for Turkey, who had trailed to a Daniel Agger penalty at the break following an abject first-half display.
However, Olcay Sahan drew Fatih Terim's side level 10 minutes after the interval and Tufan had the final say to take Turkey into their first Euro 2016 qualifier in Iceland on the back of a win.
Denmark completely controlled the opening half of the match, but only took a one-goal lead into half-time courtesy of Agger's 33rd-minute spot-kick.
Nicolai Boilesen was felled in the area by Ahmet Ozek and captain Agger, who made an emotional return to first club Brondby from Liverpool last week, stepped up to send Onur Kivrak the wrong way.
A lacklustre Turkey side - shorn of rested star names Arda Turan and Hakan Calhanoglu, who were both on the bench - struggled to cope with Denmark in the opening stages, although the hosts found it tough to penetrate Terim's compact team.
Predictably, playmaker Christian Eriksen was the man to carve out the hosts' first chance of the game after nine minutes.
The Tottenham attacking midfielder produced a typically precise free-kick delivery from the right that was only cleared to Agger, whose goal-bound right-footed shot was blocked.
Denmark's other dangerman, Lasse Schone, was next to create an opportunity, but Bayern Munich teenager Pierre Emil Hojbjerg could only fire over the crossbar from 15 yards following a low cross.
Peter Ankersen then forced Kivrak into a decent save as the hosts continued to press, but it took Agger's cool penalty just after the half-hour mark to break the deadlock.
Despite Denmark's dominance, Sahan should have equalised just six minutes after Agger's opener, but he blazed over the top after Ankersen had made a mess of a clearance.
But the Besiktas man made amends shortly after half-time when he drew Turkey level with a smart finish in the 55th minute.
Sahan raced onto Olcan Adin's well-weighted pass, wrong-footed Leon Andreasen and calmly placed his shot beyond Schmeichel.
Chances were few and far between after Sahan's strike, although the introduction of winger Turan just after the hour improved Turkey.
And it was the Atletico Madrid man who fed Tufan to strike the winner in injury time, the youngster taking aim and rifling past the helpless Schmeichel to give his side an unlikely victory.