Global-mean surface temperature rapidly increased 0.29 ± 0.04 K from 2022 to 2023. Such a large interannual global warming spike is not unprecedented in the observational record, with a previous instance occurring in 1976–1977. However, why such large global warming spikes occur is unknown, and the rapid global warming of 2023 has led to concerns that it could have been externally driven. Here we show that climate models that are subject only to internal variability can generate such spikes, but they are an uncommon occurrence (p = 1.6 % ± 0.1 %). However, when a prolonged La Niña immediately precedes an El Niño in the simulations, as occurred in nature in 1976–1977 and 2022–2023, such spikes become much more common (p = 10.3 % ± 0.4 %). Furthermore, we find that nearly all simulated spikes (p = 88.5 % ± 0.3 %) are associated with El Niño occurring that year. Thus, our results underscore the importance of the El Niño–Southern Oscillation in driving the occurrence of global warming spikes such as the one in 2023, without needing to invoke anthropogenic forcing, such as changes in atmospheric concentrations of greenhouse gases or aerosols, as an explanation.