A key innovation may allow one group of species to radiate and replace another, but the role of competition and background extinctions for the replacement process is vigorously debated and unclear. We used an individual-based eco-evolutionary model of a co-evolving competitive community to study these macroevolutionary processes. Evolutionary innovation was modeled as a heritable competitive advantage introduced in one of the co-evolved species. We demonstrate that replacement may occur by the adaptive radiation of a competitively superior group. Increasing the competitive advantage shortened replacement times, but there was no particular threshold advantage. Origination rates in new groups were comparable to extinction rates of the original groups, keeping the total number of species approximately constant over time. Extra background extinctions sped up the process, consistent with observed patterns in the fossil record that replacement is sped up during mass extinctions. The replacement process was mainly driven by evolutionary competitive exclusion. The old, inferior type had an elevated rate of extinction matched by an increased speciation rate of the superior type. Incumbency also played a role, but we found little support for a strict incumbent replacement scenario, where replacement is entirely driven by background extinctions of the old group and opportunistic speciations of the new group. Compared to adaptive radiation into an empty niche space, replacement was slow and relict species from the original group could linger in marginal and previously unexploited niche space that provided a niche refuge and prevented complete replacement. Similar patterns are also found in the fossil record.