Leoards were down to 10-men in the 27th minute when they had Luvhengo Mungomeni sent off for a second bookable offence.
This was Cosmos coach Jomo Sono's 500th game in charge.
Sono is the longest serving manager in the League, his time on the Cosmos bench in the top flight stretching back to 1995.
Sono, who has owned the club since 1983, took over the reigns himself from Roy Matthews after the club dropped down to the second division in 1994.
It is the 13th season in charge for Sono, a record only matched by Budgie Byrne when was in charge at Hellenic.
But Byrne had several broken spells with the Cape Town club and nowhere near the continuous run that Sono has enjoyed.
The 500 games are both League and Cup matches combined.
Chances were few and far between, but Cosmos' Geofrey Massa shot wide from within the penalty area just a few minutes after Mungomeni had been dismissed.
Morgan Gould then tested Leopards' keeper Mashudu Mamphitha from a direct free kick just before half time.
After the break, Leopards, despite their numerical disadvantage, were the better team although they failed to take advantage of the few chances they created against the tough Cosmos defence.
Hlompho Kekana, Eric Ramavhale and Jabulani Maluleke all shot wide with their efforts in the final third of the game.
The best scoring opportunity fell to Robert Ng'ambi late in the second half when he was one-on-one with Avril Phali but hammered his shot straight into the keepers’ hands.
The draw sees both Leopards and Cosmos move to 13 points, but their positions in the bottom quarter of the Absa Premiership remain intact.