Tuncay came off the bench at the Britannia Stadium and netted a sublime 81st-minute equaliser before Javier Hernandez's second goal of the contest sealed a 2-1 victory for the visitors.
The Turkey international looks set to make Pulis' first XI for the Carling Cup last-16 tie at West Ham as he did in the previous two rounds, but he has not started any other games for the Potters this season.
Reports suggested that, having been omitted from the squad to face Bolton in the Barclays Premier League earlier this month, the 28-year-old left the Reebok Stadium in a taxi just prior to kick-off.
Pulis has played down talk of a rift with the player, but wants to see Tuncay produce the kind of magic he did against United on a more regular basis.
"It was a great goal when we needed a bit of inspiration," Pulis told Stoke`s official website.
"He can produce things like that, but he needs to do that more often for us. People have asked me if there is a problem with Tunny; there isn't. He's as good as gold and he's a great lad to have around the place."