The defender opened the scoring in the 32nd minute, rising unmarked to power home a header from a corner after Frederick Asare had denied him moments earlier.
Matuludi then repeated the feat shortly after the restart, finding the net with another header in the 66th minute to register his first brace for the Tshwane giants.
Miguel Cardoso's side had started on the front foot, with Cassius Mailula forcing an excellent save from Asare in the ninth minute.
Durban City had an opportunity of their own when Ethan Brooks fired over from inside the box, but Ricardo Goss enjoyed a relatively quiet afternoon as the visitors struggled to create clear-cut chances.
Matuludi came close to completing his hat-trick in the 73rd minute, while Siyanda Ndlovu was also denied by Asare following a swift counter-attack. Substitute Iqraam Rayners eventually made it 3-0 in the 79th minute, converting Ndlovu's cross.
Jean Lwamba pulled one back for Durban City in the 86th minute with a clinical close-range finish, but Antonio Van Wyk restored the three-goal margin in stoppage time, scoring with virtually the final kick of the contest.
Cardoso made several alterations to his starting XI following the 1-0 Carling Knockout victory over Marumo Gallants, with Matuludi, Mailula and several other regular starters returning.
Sundowns now have 26 points from 10 matches, moving one point clear of Orlando Pirates, who have a game in hand after briefly occupying first place.