The spread and impact of invasive species may vary over time in relation to changes in the species itself, the biological community of which it is part, or external controls on the system. Here we investigate whether there have been changes in dynamic regimes over the last 20 years of two invasive species in the Midwestern US, the multicolored Asian lady beetle Harmonia axyridis and the soybean aphid, Aphis glycines. We show by model selection that after its 1993 invasion into the American Midwest, the year-to-year population dynamics of H. axyridis were initially governed by a logistic rule supporting gradual rise to a stable carrying capacity. After invasion of the soybean aphid in 2000, food resources at the landscape level became abundant, supporting a higher year-to-year growth rate, and a higher but unstable carrying capacity, with 2-year cycles in both aphid and lady beetle abundance as a consequence. During 2005-2007, farmers in the Midwest progressively increased their use of insecticides for managing A. glycines, combining prophylactic seed treatment with curative spraying based on thresholds. This human intervention dramatically reduced the soybean aphid as a major food resource for H. axyridis at landscape level, and corresponded to a reverse shift towards the original logistic rule for year-to-year dynamics. Thus, we document a short episode of major predator-prey fluctuations in an important agricultural system resulting from two biological invasions that were apparently damped by widespread insecticide use. Recent advances in development of plant resistance to A. glycines in soybeans may mitigate the need for pesticidal control and achieve the same stabilization of pest and predator populations at lower cost and environmental burden.