New Zealand's fifth rider, Jonelle Richards, finished on 56.50 penalties on Flintstar to leave her in 23rd. She made only one mistake with the extended canter when Flintstar panicked but Richards did well to keep him under control for the rest of the test considering how nervous her mount looked.
It left the New Zealand team in a good position heading into the second day of dressage.
They will hope they don't have to rely on Richards' score - the top three riders from each country count in the team's event - but a lot can happen in both the cross country and show jumping phases.
Richards also has an important job as the first rider on the team, meaning she can report back to the others on how the cross country is riding and pitfalls to look out for.
"The obvious mistake was disappointing but that is what he's capable of,'' Richards said of her test. "It's no real secret, it is his weak phase. Everything has to go our way really for it to be fantastic but, aside from the mistake, we were really pleased with it.''
Paget is one of the promising riders emerging in New Zealand eventing and wasn't overawed by the occasion.
"The fact that it's called the Olympics makes it a little more special but it's the same size arena we always go into,'' he said. "It's just there are a lot of people watching. We have had a chance to do that in Germany and the World Games. I this had been my first time in a major arena, it would have been very daunting.
"There's a lot of work to be done. I need to walk the course a bunch of times so I know my lines and try to be like a Formula 1 car out there.
"If I can finish on my dressage score, I think it will be up there. It's going to all depend on tomorrow and there are a lot of good combinations to come.''
They include Todd and Nicholson but also Britain's William Fox-Pitt and Zara Phillips and world champion Michael Jung of Germany.
The cross country will be ridden on Monday night (NZT), with the show jumping the following day.