The Urban Warriors had opportunities to score more goals on day, but Prince Nxumalo amongst others failed to convert their chances.
Dikwena tried to get back into the game with the introduction of strikers Henrico Botes and Ndumiso Mabena, but they struggled to penetrate the stubborn Urban Warriors defence.
Ajax's victory also sees them move further away from the relegation zone on the league table.
The hosts drew first blood through Mzwanele Mahashe seven minutes into the game, but they could not score more goals and the match ended in a 1-1 draw with Lyle Lakay scoring for Celtic.
It's the second time in as many league games that Bakgaga have dropped two points in the closing stages of the game.
They drew 1-1 with Orlando Pirates after Issa Sarr scored very late in Soweto in midweek.