The Springbok captain expects a desperate performance from New Zealand in Saturday's decider in Baltimore as they look to square the series, but said their desire to secure a 3-1 victory is just as strong.
The match will also mark Rassie Erasmus' 100th Test match in his two roles with the Springboks since joining the team in 2018, first as head coach and later as Director of Rugby.
"We definitely want to win the series," said Kolisi.
"We don't want to draw it, and that has been our mindset this week. The All Blacks have brought in new players and we've had to look at them and what they could bring differently this weekend, so we've done our homework.
"But the key thing for us will be to make sure we enforce our game on them, and pitch up physically on the day.
"We've all seen in the last three games that if you are not at your best, they have what it takes to punish you. But so do we, and we want to make sure we keep making our people proud."
Kolisi admitted it doesn't get more challenging than having to face the All Blacks four times in a row, likening the experience to playing four straight World Cup finals.
"We're growing and learning on the go, because it is a tough series and we're playing the same opposition four times in a row.
"They get to know you, and you get to know them, so you have to find other ways and other weaknesses. This week we're playing almost a new All Blacks team compared to last week, and Richie Mo'unga brings a different dynamic, so it might be different from the other games.
"In my experience, it doesn't get tougher than this. It's like playing four Rugby World Cup finals in as many weeks, given the quality of both teams. We both want to enforce our style of play on the game.
"We may be leading the series, but we know on the other side they are desperate to level it up, so we want to make sure we finish properly tomorrow."
Assistant coach Mzwandile Stick was thrilled to see all the Springbok supporters in Baltimore, many of whom are expats who have travelled from different states in the USA to attend the match in Maryland.
"There are a lot of South Africans here and the vibe is great, so we are excited about the opportunity to promote rugby in the USA," he said. "Everywhere you go around the hotel you see green and gold and people are proud to see us, so we want to make sure we represent them and put up a good show."
Saturday's match in Baltimore kicks off at 11pm.