Conditions were near perfect for racing on Saturday and the elite field was the strongest it has been in the seven-year history of the event.
Bowman said it was very satisfying to cross the line in first, and he rated the win as the best of his career.
"It is my first international race that went well and this is a very high-profile event, so I really wanted to have a strong performance," he said.
"It helps establish myself on the international scene and this is my life, so when something goes well like this it is very satisfying."
Bowman was back on the finish line 16 minutes after winning the race to greet his good friend Jorge Maravilla, who finished second.
The pair are from the same city in California, Mill Valley, and train together. "He is one of my best buds," Bowman said.
Bowman said he took the lead about 40km into the race and decided to try and break away. He was never caught after the move.
"I just caught the leader and at that point you have to commit." Japan's Yoshikazu Hara finished third, 27 minutes behind the winner.
In the women's race, Muir had a tight battle with fellow Kiwi Ruth Croft.
After leading for most of the race, Muir was caught by Croft with about 10km to go in the race.
"I thought it was over, I was feeling pretty low at that point but when she came parallel with me I thought 'this is not happening' and went for it."
Muir said she discovered some energy from somewhere and managed to pull away and win the race.
"I have never felt that before, I did a lot of road running in my training and I think that helped a lot."
Muir finished 12 minutes ahead of Croft with world champion Nuria Picas-Albets (Spain) finishing in third, 38 minutes back from the winner.
More than 1100 runners were entered for the race on Saturday across three distances - 100km, 85km and 60km - for teams and individuals.
The Tarawera Ultramarathon was the second stop on the 11-race Ultra-Trail World Tour.
