The win, which was AmaTuks' first of the season, moves them up to eighth spot on the log while Siwelele slide down to 11th.
Three debutants were involved from the onset, two for the University of Pretoria and one for Bloemfontein Celtic.
Massa and Nyondo started up front for Tuks while Clayton Daniels, who was released by Mamelodi Sundowns earlier this month, started for Siwelele.
Tuks opened the scoring in the 16th minute through Nyondo, who beat the onrushing Patrick Tignyemb to a hopeful ball before slotting the ball into the back of the net.
Two minutes later Massa doubled the home side’s lead with a fierce free-kick – an excellent effort which left Tignyemb with no chance.
Joel Mogorosi, who has been in great form of late, had two opportunities to pull one back for Celtic six minutes before the break. However, he was left frustrated after a brilliant tackle from Grant Kekana before a follow-up effort which Washington Arubi saved from point blank range.
Siwelele came out firing after the break and should have narrowed the deficit in the 52nd minute.
Musa Nyatama, who had been troubling the Tuks defence throughout the afternoon, found himself in a one-on-one situation, but was denied by Arubi.
Celtic had several other opportunities towards the end of the encounter to get on the score sheet, but a combination of poor finishing and good defending meant they left Tshwane goalless.