Tuncay came off the bench at the Britannia Stadium on Sunday 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 Wednesday's 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 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 the club'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."
Tuncay has seen his chances limited at Stoke this term by the impact of new arrivals Kenwyne Jones and Jon Walters, and with Ricardo Fuller also in the mix up front, Pulis is delighted to see the competition for a starting berth heating up.
"It's vital that we have strength in depth and competition for places in all departments because it is very much a squad game," Pulis said.
"We have a good group of strikers here now capable of giving us more goals, but they have to take their chance when they are called up."
Pulis is likely to make several changes for the trip to Upton Park, with some players picking up knocks in Sunday's game, Marc Wilson cup-tied and Dean Whitehead available again after serving a one-match suspension.
The manager will be fielding a side he believes can win, though, as the Potters look to overcome the Premier League's bottom side and secure a place in the quarter-finals.
"Although we will make one or two changes, we will go there and try to win the game," Pulis said.
"It will be tough because, despite their current position, they have some quality players and we must respect that."