Midfielder Lebese scored a scrappy goal on 42 minutes in Soweto to give title-holders Chiefs a 1-0 semi-final, second-leg win over Bloemfontein Celtic.
That was sufficient to see the Amakhosi (Chiefs) through after they came from behind two weekends ago to earn a 1-1 first-leg draw.
Veteran striker Paulse bravely converted a 25th-minute penalty to deliver a 1-0 victory for Ajax over 10-man Wits in Johannesburg.
Ajax also advanced 2-1 on aggregate after Wits came from behind in Cape Town 15 days ago to snatch a 1-1 draw on a muddy mess of a pitch.
Neither second leg rose above the ordinary with Celtic lacking attacking sharpness before a 35,000 Soccer City stadium crowd.
A quick exchange of short passes found Lebese with the ball inside the box and although surrounded by a posse of Celtic defenders, he scored with a low shot into the far corner.
Wits full-back Siyabonga Nhlapo was red-carded for the foul that led to the tie-deciding penalty and great goalkeeping by Moneeb Josephs prevented a heavier defeat for the hosts.
Paulse, who ranks among the tallest footballers in South Africa, gambled by firing his penalty down the middle, but succeeded because Josephs dived to his left.
The scorer opted not to take another penalty, late in the second half, and Josephs dived to push away a timid effort by Cecil Lolo at Bidvest Stadium.
An early-season knockout competition, the Top 8 is contested by the top eight league finishers of the previous campaign and offers an eight million rand ($600,000, 540,000 euros) winners-take-all prize.
CAF Confederation Cup title-holders receive $60,000 more, but play a minimum of 16 matches compared to the four of Top 8 winners.