The Black Cats manager admitted he will try to tempt the South Korean into making a full-time move to the north east.
The victory lifted Poyet's men off the foot of the table, and the Uruguayan said the better Sunderland's form is the more chance he has of convincing Swansea loanee Ki to sign long-term.
"There is a chance (of a full transfer)," said Poyet.
"Swansea had an opportunity to call him back, and they didn't. That was a difficult day for me because I was waiting and waiting.
"I think there are a couple of things we need to make sure: where we are and where we want to go, and with the player as well.
"I can see that he's enjoying his football and making a difference."
Ki is on a season-long loan at the Stadium of Light, but Swansea boss Michael Laudrup seriously considered recalling the 24-year-old last week, to ease a midfield injury crisis.
But the Dane decided against it, leaving Poyet as relieved as he was delighted.
"At least we still have him, I was nervous in that time," said the former midfielder.
"He's very happy, it means so much for him to score that goal. He cares and he's enjoying his new position a bit further up the pitch and making a difference.
"I want players with that mentality, to make us play, and he's been excellent. He's been the most consistent player for me, in my way of playing.
"Then of course John O'Shea and Wes Brown at the back, we're more solid and pressing some of the space.
"The basics are there then hopefully, if we can keep them all fit."
While most managers embroiled in relegation skirmishes have bemoaned the Christmas fixture pile-up, Poyet has taken a novel approach.
Refusing to rotate his squad, the Sunderland boss has kept training as light as humanly possible.
The result is three straight victories, including a 2-1 home win over Manchester United in the Capital One Cup.
"You can play but you can't train," said Poyet.
"If you really want to coach you need to train. But when you play, play, play, recover, then play again, then everything you do in preparation is mental.
"So it's all mental, and information that you are giving the players, but you are not training things and improving things. So for the coach it's difficult.
"For the players it's spectacular, I loved it. When I was a player I just wanted to play, I didn't want to train.
"It's all about talking and talking, because you cannot really train them hard.
"That's the way it is for everyone though. It's working for us at the moment though, so I can't complain!"
He added: "I've never been a fan of the rotation system, I don't like it.
"I know sometimes you have to change because there are too many games, especially if there's one game two days after another.
"But if you look at the last four or five games, there are eight players that have been there most of the time.
"So there are only two or three places up for grabs.
"And that brings consistency, and a better quality of training too. I think we are in a better situation, more consistent."
- Sports & Recreation