The Urban Warriors were the better side for most of the match, especially in the opening exchanges, with the likes of Bantu Mzwakali, Cecil Lolo and Paulse too hot to handle for the Amakhosi defence.
Ajax looked to have opened the scoring in the 24th minute when Musa Lebusa had the ball in the back of the net from a free-kick. His run was timed perfectly, but Paulse interfered from an offside position and the goal was ruled out.
Eight minutes later, a beautiful set-piece by Mzwakali picked out Paulse in the box, but his volley rattled the woodwork with Itumeleng Khune beaten.
Lolo then fired a long-range effort just wide as Chiefs failed to register a single shot on target in the first half.
Roger De Sa’s men continued where they left off and were rewarded with a penalty in the 55th minute after Paulse was adjudged to have been fouled by Erick Mathoho in the box.
Paulse made no mistake as he beat Khune from the spot.
Amakhosi continued to probe for an equaliser but could not break down the Ajax defence, who were working their socks off in midfield to break down any attack.
Chiefs finally got their chance in time added on, when Willard Katsande met a corner-kick that looked destined for the far corner, but Anssi Jaakkola produced a world-class save to win the match for his team.