Willis ran a time of 3:40.92, well short of his personal best but enough to win a slow heat.
The semifinals take place on Monday morning.
Nixon Chepseba, the only other person to run faster than Willis this season, failed to make the semis after he finished ninth in the same heat as Willis.
Willis told Sky Sports that tactics worked to deny his rival a spot in the semis.
"I got through and win my heat and managed to use tactics to eliminate one of my key rivals along the way. I boxed him in at the bell and he got caught up amongst the crowd," he said.
"It didn't feel quite as effortless as I thought it might. I thought I'd scoot away a bit in the last 100m. So a faster pace suits me a lot better."
"It was a lot of fun. The crowd was actually really receptive to a Kiwi. Perhaps because they didn't have any Brits in the race."
