Siwelele were fresh from a 2-1 win over Super Eagles in the Nedbank Cup round of 32 match last weekend and they were hoping to erase their loss in the PSL.
Celtic had succumbed to a 2-1 loss to SuperSport United in their last league match.
Ronald Pfumbidzai opened the scoring as early as the seventh minute to make it 1-0 to Celtic. Siwelele were leading at half-time and they upped the ante in the second half and Victor Letsoalo scored twice in the dying stages to seal Celtic's 3-0 win.
The victory took the Free State-based outfit to the fifth spot with 28 points from 19 league games, while Leopards are placed 12th with 20 points from 18 matches.
The hosts were looking to secure a victory after losing 1-0 to Jomo Cosmos in the Nedbank Cup during the week.
On the other hand, the Chilli Boys were still in high spirits after beating Mamelodi Sundowns in the Nedbank Cup last weekend.
Although the score was 0-0 at half-time, Baroka midfielder Walter Mabeba scored with 20 minutes to go, but his team-mate Bonginkosi Makume netted an own goal a minute later and it was ensured that the match ended in a 1-1 draw.
The result saw Baroka remain 13th on the league standings with 17 points from 19 league games, while the Chilli Boys sit a spot below with 16 points from 19 matches.