To develop public-health policies that extend the lifespan of affordable anti-malarial drugs as effective treatment options, it is necessary to understand the evolutionary processes leading to the origin and spread of mutations conferring drug resistance in malarial parasites. We built a population-genetic model for the emergence of resistance under combination drug therapy. Reproductive cycles of parasites are specified by their absolute fitness determined by clinical parameters, thus coupling the evolutionary-genetic with population-dynamic processes. Initial mutations confer only partial drug-resistance. Therefore, mutant parasites rarely survive combination therapy and within-host competition is very weak among parasites. The model focuses on the early phase of such unsuccessful recurrent mutations. This ends in the rare event of mutants enriching in an infected individual from which the successful spread of resistance over the entire population is initiated. By computer simulations, the waiting time until the establishment of resistant parasites is analysed. Resistance spreads quickly following the first appearance of a host infected predominantly by mutant parasites. This occurs either through a rare transmission of a resistant parasite to an uninfected host or through a rare failure of drugs in removing "transient" mutant alleles. The emergence of resistance is delayed with lower mutation rate, earlier treatment, higher metabolic cost of resistance, longer duration of high drug dose, and higher drug efficacy causing a stronger reduction in the sensitive and resistant parasites' fitnesses. Overall, contrary to other studies' proposition, the current model based on absolute fitness suggests that aggressive drug treatment delays the emergence of drug resistance.