The Black Cats could have moved out of the bottom three with a win at Cardiff City Stadium, but instead found themselves blown away by a Bluebirds onslaught during the first hour and trailed 2-0 to goals from Jordon Mutch and Fraizer Campbell.
But as Cardiff retreated into their shell during the latter stages, the Wearsiders came on strong and struck through Steven Fletcher and Jack Colback, the latter deep in stoppage time, to earn a point.
Poyet's side still sit at the bottom of the Premier League table heading into the new year, a position which historically has tended to signify a one-way ticket to the Championship.
But having ensured they are no longer adrift of their rivals, the Uruguayan believes they will be in the top flight next term.
He said: "I do feel we will be in the Premier League next season because we are back there with the other teams. When I took over there was a big gap to the teams in the middle of the table, now we are one win away from getting out of the relegation zone.
"That is a great feeling for the players and the fans. It is now up to us, we are five games unbeaten.
"When you are at the bottom people do not notice that, but we had been defending well until this game and we scored today.
"We are going in the right direction so let's hope we can maintain that consistency in the New Year and get another three points.
"We have character and desire and we are going to fight."