Menjo, who heads the year's 10,000m rankings, ran the last half of the race on his own at Melbourne's Olympic Park to finish in 27 minutes 39.80 seconds.
It was the fastest time recorded at the Zatopek event in 12 years, while the winning margin of 26 seconds was the biggest since 2002.
"I am happy with my time as it is December and I haven't been training for this," Menjo said.
"I slowed down to try and take them with me at 5000m but they didn't come." Australian Ben St Lawrence was second in 28:05.25, while American Bobby Curtis was third in 28:08.78. Kenyan Luke Kipkosgei was in fifth place.