Steamers head coach Mike Delany said the effort came down to efficiency in their systems and good discipline across the park.
"We are pretty happy with coming away with 5 points," Delany said.
"We got our game going a bit earlier, and less unforced errors and penalties put us in a pretty good place. The likes of Kaleb Trask helped drive us around the park well."
"We've had a really good week of preparation, after one win we can't get too comfortable, so it's going to be a good test of where the team is at."
Delany said everyone had played their part in the match against Taranaki.
"It was a real team performance. Our forwards put a massive platform up that enabled our backs to get going and get some space.
"It was awesome to see the likes of Emoni Narawa, Joey Walton and our back three with freedom on those edges."
Notable changes to the starting XV in Eden Park include All Black Aidan Ross returning to the side to form a formidable front row with Captain Kurt Eklund and Tevita Mafileo.
Scottish national Jamie Dobie, who made his debut against Taranaki, will also move into the starting line-up for his first start of the season.
"There's been an edge to the boys at training," Delany said.
"It's been a while since we've left Eden Park with a win, we've done everything we can this week to ensure we put a performance up that we can be proud of."
Delany said the boys were excited for the chance to play for the John Drake Memorial Trophy.
John Drake was an Auckland provincial legend who played eight games for the All Blacks.
After retiring from rugby, Drake quickly rose the media ranks as a columnist and TV personality.
When asked about the famous game of 04 being the last time the Steamers beat Auckland at Eden Park, Delany said the opportunity to create a bit of history excited the team.
"Aidan Ross touched upon it [2004 Ranfurly Shield match] with the boys at the start of the week, how long it had been.
"There's a real opportunity with the group that we've got to get the job done.
"There's real confidence in the group, but we know how hard the challenge will be. We are excited to get out on Eden Park."