The Wallabies all but killed off the Springboks' title hopes with a 30-13 victory at Lang Park, attacking fiercely to build a big halftime lead and then quelling a second-half fightback with some fierce tackling and ball-pilfering at the breakdown.
"Gotta be happy with the performance, there's a lot of stuff to be proud of. Particularly the defence," Deans told reporters.
"The start to the game I guess set the scene where the boys were prepared to work hard and that was critical to get the foot in the door.
"Clearly the Springboks ... were desperate, they threw everything at us and the boys stood the test of time," added Deans who rated the defensive effort the best during his tenure.
Despite the emphatic win, in which Australia showcased a rarely-seen aggression to complement their nippy ball-carrying game, the hosts missed a number of chances to put the match beyond the opposition.
Ball-fumbling, ill-directed passes and poor decision-making ruined a number of scoring chances, leaving the team with only two tries by Drew Mitchell and Will Genia despite the lion's share of possession.
Mitchell's try epitomised the bungling, the winger juggling the ball three times as he spun across the goal-line before planting it in the turf to put the Wallabies 17-3 up at halftime.
"We created some opportunities that we didn't finish and that's always frustrating," said New Zealander Deans, whose side face a rampant All Blacks in Melbourne next week.
New Zealand thrashed South Africa 32-12 in Auckland and 31-17 in Wellington to secure two bonus points from their opening two Tri-Nations matches.
"We'll recover and we know next week that we've got a team coming who will do that plus a bit. They have a lot of patience so they'll work us around and we'll have to finish the opportunities that we get," added Deans.
(Editing by Tony Jimenez. To query or comment on this story email email@example.com)