Nascimento has signed a three-year-deal with the defending Absa Premiership champions while 22-year-old midfielder Mkhulise signed a five-year-deal.
Nascimento joined 2016 and made 50 appearances for Sundowns. While Mkhulise was brought into the first team at the start of the 2018/2019 season.
The South American defender was linked with a move away from the Pretoria side before the start of the season, which is said to be the reason why he stormed off the field after he exchanged words with a referee during the 0-0 draw against Highlands Park last month.
Sundowns announced the new deals on their Twitter account.