The emphatic win at Loftus Versfeld also saw loose forward Anton Segner emerge as a star in the making, with the 25-year-old delivering an outstanding performance.
The openside flanker, who made his Test debut last month, was named man of the match after impressing with his pace, strength, defensive ability and work rate.
Segner could now push Luke Jacobson for a place in the match-day squad when the All Blacks face the Springboks in their first Test in Johannesburg next week.
Centre Rieko Ioane was another standout performer as the All Blacks ran in eight tries to three against a Bulls side that played with plenty of adventure and skill, particularly in the second half.
Ioane looked re-energised on his return to the side following his sabbatical, with his form coming at a crucial time after Billy Proctor returned to New Zealand with a fractured shoulder blade.
The All Blacks also showed significant improvement at scrum time, with props Xavier Numia and Tyrel Lomax making a strong impact, supported by locks Fabian Holland and Patrick Tuipulotu.
Holland continued his impressive tour with another lively performance, including an excellent offload that put captain Codie Taylor over for his second try.
He also made his presence felt at the breakdown, an area where the All Blacks applied considerable pressure on the Bulls.
Their maul defence was also much improved, with the visitors shutting down several Bulls attacks close to their try line.
The All Blacks conceded just eight penalties, showing better discipline than in their earlier wins over the Stormers and Sharks.
The Bulls, meanwhile, were reduced to 14 men after prop Francois Klopper was sin-binned for a cynical offside after 30 minutes.
The All Blacks were generally clinical inside the Bulls' 22, although some of their finishing when attacking from deep left room for improvement.
Head coach Dave Rennie said afterwards that his side's performance was "mixed".
He said the All Blacks also needed to improve their offloading, particularly in the wet conditions.
Rennie also provided an update on the fitness of backs Cam Roigard and Will Jordan, who have yet to feature on tour, saying he was confident both would be available for the first Test.
Damian McKenzie, however, remains a greater concern after suffering an ankle sprain against the Sharks, although Rennie said he was confident the fullback would recover.
Taylor's return from a calf injury will also please the All Blacks coach, with the captain playing 40 minutes and scoring two tries.
Josh Moorby and Leroy Carter also scored two tries each, while Ioane and replacement loose forward Wallace Sititi were the other try scorers.
The All Blacks now turn their attention to the Springboks, whom they will face next Sunday at 3am.
Source: 1News
