The winning margins were slightly flattering - the Kiwis let big leads slip in both races, but still recovered their poise for easy victories, which is probably an indication of how quickly things can change in this form of racing.
"It's no secret, to win the America's Cup, in our case, you have to win eight races," said Burling afterwards. "We're really happy to get two races on the board early, but we're under no illusions it's going to get a lot harder than that and it was relatively hard today.
"If there's one thing these guys have shown, they fight incredibly hard and we're just preparing for that battle over the next couple of days.
"It was really fun yachting out there - it felt like our boat was going really fast, which was really pleasing - but we definitely had a lot of issues on board today to let them back in the game.
"We were really happy with the composure the guys showed to hold onto those leads and convert them."
Of course, Oracle skipper Jimmy Spithill led the historic comeback from 8-1 down to defend the Auld Mug in San Francisco four years ago, so he knows how to come back from an early deficit.
But Team NZ also showed they were capable of mistakes that could let the US syndicate back in the hunt, even when they seemed to be dominating.
In the opening race, they rounded the final mark 55 seconds ahead, but fell off their foils and had to regroup, eventually finishing just 30 seconds up. It was a moment reminiscent of their one-second victory over Artemis Racing in the challenger final series.
"It wasn't actually our best manoeuvre," admitted Burling. "It actually reminded me of the one we had against Artemis, where we had an incredibly tight finish.
"The really pleasing thing out of it was, when everyone did scramble, we still managed to get the job done, no worries. We're really happy with the way the guys kept their composure today.
"It's no secret that it was a really tricky day out there and if you made a small mistake, it ends up being a really costly one, which I think Oracle showed in that last race.
"We're really excited with where we checked in today, but under no illusions we've got a lot of hard work to do over the next week or so to keep improving, keep pushing forward, because we know that's exactly what these guys will be doing."
In the second race, Team NZ built a lead of more than a minute, but failed to cover their opponents up the fifth beat and watched that advantage dwindle to just a few metres.
Oracle actually protested that the Kiwis had not allowed enough space around the top mark, but no penalty was imposed.
Immediately after the gate, Spithill blew a gybe that saw his boat fall off its foils and concede all the ground it had made up previously.
"It was an interesting end to that beat," said Burling. "Like we've been saying, it's incredibly puffy and shifty and tricky out there, and the really pleasing thing for us is how the guys on board held their composure and executed what we had to do to stay in front.
"We definitely lost a lot - we did some bad manoeuvres and got stuck in some pretty light breeze, but then ... to be able to pull off that last tack and get round that mark first definitely sealed that last race for us."
Burling admitted he probably should have covered Oracle up that fifth beat and emphasised his team would be reviewing their performance closely.
Two more races are scheduled for tomorrow morning (NZ Time), and then five days off before the series resumes with races five and six.
