The draw behind closed doors at Dobsonville Stadium in Soweto left the defending champions three points adrift of leaders Kaizer Chiefs with each club having eight matches to play.
It could have been an even worse outcome for Sundowns as they were outplayed in the second half by Pirates, whose Fortune Makaringe was denied a goal by the woodwork.
Makaringe burst through and his shot took the slightest of deflections off the fingertips of Ugandan goalkeeper Denis Onyango, struck the base of the post and was hastily cleared.
Pirates had another chance to collect maximum points with five minutes remaining, but a brilliant tackle by Motjeka Madisha prevented Paseka Mako shooting from close range.
After scoring three goals last Saturday in an FA Cup semi-final triumph over Bidvest Wits, Sundowns disappointed as an attacking force and rarely troubled goalkeeper Wayne Sandilands.
Chiefs have 48 points and Sundowns 45 from 22 matches and Pirates 41 from 24 in the richest African league with a 15 million rand ($860,000/730,000 euro) first prize.
Sundowns chasing treble
Sundowns are chasing a treble this season having won the League Cup and qualified for the FA Cup final against Bloemfontein Celtic on September 8.
"Our performance reflected the fact that we had not played since early March," said Pirates' German coach Josef Zinnbauer.
"We were much better in the second half and could have beaten Sundowns with a little more luck in front of goal."
Sundowns coach Pitso Mosimane said: "We had the edge during the first half but fell away after half-time and were grateful for a point in the end.
"Obviously, we wanted three points tonight, but I am satisfied with one. Pirates are a top-class team and still in contention for the title."
All league matches are being played at neutral venues in the Gauteng province, which includes Johannesburg and Pretoria, with the final round scheduled for September 5.
The Premiership is the fourth major league in Africa to resume after the Moroccan Botola Pro 1, the Tunisian Ligue Professionnelle 1 and the Egyptian Premier League.
Algeria, the Democratic Republic of Congo, Ghana, Nigeria and Senegal were among many African countries who chose not to resume football after stopping in March due to COVID-19.