The result moved Pirates to within four points of leaders Mamelodi Sundowns, with the Buccaneers still having two games in hand.
Durban City made life difficult for the hosts, who had to wait until the second half to break the deadlock.
Pirates finally found a way through in the 58th minute when Lebone Seema rose highest to head Kabelo Kgosietsile’s delivery into the net.
It was Seema’s second goal of the season after he also scored in the 3-0 victory over Chippa United in August. The defender has now scored four goals for Pirates in all competitions.
The Buccaneers doubled their advantage 11 minutes later, with Moremi producing the decisive moment.
READ: La Cure Waves coach Jerome Thomas says Orlando Pirates have enough quality to win Champions League
Simphiwe Masilela created the opening for the 22-year-old, who collected the ball on the edge of the box before curling a fine finish beyond the goalkeeper.
It was an important response from Moremi after he was overlooked for Bafana Bafana’s latest squad under new coach Mosimane, with Puso Dithejane of Chicago Fire and Tashreeq Morris of Sundowns among the forwards selected.
Moremi could only answer that disappointment on the pitch, and his goal against Durban City underlined what he can offer Pirates.
The match also produced a significant moment for Masilela, who registered the first assist of his professional career.
The victory extended Pirates’ unbeaten run in all competitions to 25 matches.
Pirates return to action on Sunday when they travel to face Marumo Gallants.