The Crusaders dominated the first half as they raced out to a 21-8 lead with Tim Bateman also crossing for a try before Mataele scored twice while Brumbies winger Chance Peni was on the sidelines for a high tackle on Israel Dagg.
The eight-times champions ruthlessly exploited their extra man advantage to put Mataele, who replaced Dagg, across twice to give them a 21-5 lead after Brumbies winger Henry Speight scored his side's only try early in the match.
The Brumbies turned the tables in the second half and were much more clinical and controlled the ball better but were unable to crack the Crusaders defence, even when Scott Barrett and Ryan Crotty were given yellow cards by referee Jaco Peyper.
Both players were penalised after the Crusaders had been given a warning from Peyper for persistent offending as they defended their line against waves of attacks from the Brumbies.
Last year's champions then slowed the pace of the game down and produced a strong defensive effort to ensure the Brumbies did not score while they had the two-man advantage and continued Australia's doldrums against New Zealand opposition.
Australian sides have not beaten a New Zealand team since the New South Wales Waratahs defeated the Waikato Chiefs 45-25 in week 14 of the competition in 2016.
Since the start of the current World Cup cycle in 2016, Australian teams have won just three games and secured one draw in the 56 Super Rugby matches between the trans-Tasman rivals.
The Crusaders moved to the top of the Super Rugby standings on 33 points, one ahead of the Wellington Hurricanes with South Africa's Lions third on 31.
The Brumbies (3-6) have topped the Australian conference for the last two years but are sitting nine points behind the New South Wales Waratahs (24), who have a bye this week.
(Reporting by Greg Stutchbury in Wellington; Editing by Ken Ferris)
