Willis sat near the back of the bunched field for most of the journey, but moved into position around the final bend and finished strongly to secure his passage.
"It felt really comfortable," he said. "I was a little sluggish ... the biggest challenge was actually getting into the race.
"There's less than a 24-hour turnaround until the semifinals, so all that mattered was getting through, using as little as possible energy.
"It was hard to get out of third gear .. but there were not as many guys challenging in the home straight as I thought there might be, so that was fortunate. I was able to jog it in the last 30 metres, without having to fight to the line."
The news was not so sweet for Angie Petty, who missed out on qualifying for the women's 800 metres by just 0.03sec.
Petty finished fourth in her heat, clocking 2min 01.76sec, and was safely among the six slowest losers, as the final heat lined up.
But the sixth heat proved the fastest, with Francine Niyonsaba of Burundi winning in 1min 59.86sec and the top seven finishing inside Petty's time. South African Gena Lofstrand took the final qualifying spot with 2min 01.73sec.
"I should have been running way better than that 2:01, but it was the way it was run ... maybe I didn't position myself really well," said Petty.
"I still gave it everything in the last 100m, but it just didn't feel like I was as sharp as I was hoping."
Distance runner Camille Buscomb and javelin exponent Ben Langton-Burnell also came up short in their attempts to qualifying for finals.
Buscomb led for the opening four laps of her 5000 metres heat, but faded when the pace went on over the second half of the race and finished 16th in 15min 40.41sec.
She admitted afterwards she had done her best performances earlier in the northern season to qualify for the 5000m and 10,000m, and was far from top form in London.
Langton-Purnell was six metres off his best, throwing 76.46m to finish 24th in javelin qualifying. He would have needed a personal best to make the top 12.
