The Springbok internationals Danie van Schalwyk and Schutte Bekker were among the try-scorers as Newport were left floundering after holding a 24-18 lead midway through the second half.
The Bulls had seen a second player, lock Derick Grobbelaar, sent to the sin-bin by the Scottish referee Iain Ramage and Newport needed to take maximum advantage. But it was the Bulls who made light of their one-man disadvantage, scoring a vital try through centre Conrad Stoltz. Stand- off Gavin Lawless' conversion meant they had regained the lead at 25-24.
Grobbelaar also touched down within three minutes of rejoining the action and flanker Nicky van der Walt made victory certain when he intercepted a pass by the Newport scrum-half Steve Moore and sprinted 40 metres.
Newport competed well throughout and despite trailing 10-3 after just seven minutes they changed ends ahead courtesy of a sparkling try by the right wing Alan Harris plus two penalties and one conversion from stand- off Shaun Connor.
The Bulls' frustrating tendency to wander deliberately offside saw Bekker sent to the sin-bin, yet Newport could never pull sufficiently clear to seriously contemplate victory.
Bridgend gained their second win in Pool B, a hard-earned 17-15 success against Gauteng Falcons. The South Africans, still seeking their first success after three matches in the competition, might easily have come away with a draw.
Three minutes into injury time the left wing Dawie Du Toit went over in the corner for the Falcons' second try, but he then failed with his conversion from the touchline. Two Falcons were sent to the sin-bin in the second half, with substitute scrum-half Awie Nel and replacement flanker Rudi Rohrs off the field at the same time.
Bridgend had been given a great start with a third-minute try by the right wing Sam Greenaway. Full-back Gareth Cull, who was replaced at half- time, converted. Falcons edged ahead with a penalty by Du Toit who also converted a 35th-minute try by the No 8 Naas Rossouw. Bridgend, who beat Romania 44-10 in their opening Trophy match, face the Blue Bulls on Sunday and then Glasgow Caledonians next Wednesday.
In Group A, Caerphilly survived a second half rally by Georgia to win 36-17 in front of a sparse crowd. Two crucial penalty tries secured the win for Caerphilly.
Aberavon claimed a deserved 20-14 victory over the Natal Wildebeests which kept alive their qualifying hopes. Natal took a sixth-minute lead through their captain and flanker Craig McIntosh, but the home side fought back and sealed victory with a 70th-minute penalty try.