Malaria, a deadly infectious disease caused by the protozoan Plasmodium, remains a major public health menace affecting at least half the human race. Although the large-scale usage of insecticides-based control measures, notably long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS), have led to a dramatic reduction of the burden of this global scourge between the period 2000 to 2015, the fact that the malaria vector (adult female Anopheles mosquito) has become resistant to all currently-available insecticides potentially makes the current laudable global effort to eradicate malaria by 2040 more challenging. This study presents a novel mathematical model, which couples malaria epidemiology with mosquito population genetics, for assessing the impact of insecticides resistance on malaria epidemiology. Numerical simulations of the model, using data relevant to malaria transmission dynamics in the Jimma Zone of Southwestern Ethiopia, show that the implementation of a control strategy based on using LLINs alone can lead to the effective control of malaria, while also effectively managing insecticide resistance, if the LLINs coverage in the community is high enough (over 90%). It is further shown that combining LLINs with IRS (both at reduced and realistically-attainable coverage levels) can lead to the aforementioned effective control of malaria and effective management of insecticide resistance if their coverage levels lie within a certain effective control window in the LLINs-IRS coverage parameter space (this result generally holds regardless of whether or not larviciding is implemented in the community). The study identifies three key parameters of the model that negatively affect the size of the effective control window, namely parameters related with the coverage level of larviciding, the number of new adult mosquitoes that are females and the initial size of the frequency of resistant allele in the community. For the coverage of LLINs and IRS within the effective control window, an additional increase in the values of the aforementioned three parameters may lead to a shrinkage in the size of the effective control window (thereby causing the failure of the insecticides-based control).