The 28-year-old is a genuine contender after an injury-free season.
Willis was last for the first two laps before surging to join Kiplagat in the lead at the bell. He says a strong wind was troubling a number of competitors but he knew if he moved to the front for the final lap, he could challenge.
"I'm not sure I was ever in the hunt for the win but it is better for my belief against these guys if I can match them throughout the race and execute a decent race plan. I am matching what the best in the world have to offer. The X-factor is coming back to my racing, just like in Olympic year, and it's not something I'm taking for granted [after injuries the last couple of seasons]. I've had good health and consistent training this season.
"I'm probably one to two seconds faster than I was in 2008, but back then I was helped by some competitors not being at their best."
Willis knows from this phase of the campaign he can now race at a faster pace but is mindful big meets such as the Olympic Games and world championships do not have pacemakers, something that can work in his favour, provided it slows the race slightly.
Willis notes the Olympic record is a relatively slow 3m 32.07s, set in 2000 by Kenyan Noah Ngeny. The world championship record is lower at 3m 27.65s but a key reason middle distance great Hicham El Guerrouj ran that in 1999 was because a countryman sacrificed himself over the first couple of laps to set him up.
"It's exciting that a faster race could now suit me," Willis says. "But with hot, humid conditions expected in Daegu, the pace might be slower unless the Kenyan contingent decide otherwise."
At the same meet, Stuart Farquhar was third in the javelin with a throw of 84.21m. That places him 16th best in the world this year and gave him an A standard qualifying throw for the world championships.
Also in Stockholm, Val Adams continued her return to top form in the shot put, with 20.57m. It was 20cm better than rival Nadzeya Ostapchuk.