The cortisol awakening response (CAR) is thought to represent an anticipatory mechanism to prepare for upcoming demands. In sport, competition increases in the CAR have been reported, although findings remain inconsistent. A study on amateur athletes identified a divergent CAR between individual-sport (IS) and team-sport (TS) athletes, thereby highlighting sport type as a confounding factor. Our aim was to determine whether competition-related changes in the CAR are robust in elite athletes and whether sport type moderates this response. Using a within-subject crossover design, 190 elite athletes (58 women) from seven sports (soccer, field hockey, handball, badminton, athletics, swimming, and judo) provided saliva samples upon awakening (T0) and 30 min after awakening (T30) on both a competition day and a rest day. The CAR was quantified as a change score (T30 − T0) based on log-transformed and raw values. Both sets of analyses revealed a significant trial effect (p < 0.001). The CAR was greater on competition days (back-transformed mean = 82.1%, 4.81 ng/mL raw units) than on resting days (mean = 24.7%, 0.99 ng/mL), representing large effect size differences. No significant effect of sport type, nor a trial × sport type interaction, was detected. In conclusion, we observed a robust elevation in CAR on competition mornings in elite athletes, compatible with anticipatory processes and potential training-related influences. In contrast to findings in amateur athletes, the CAR did not differ between IS and TS athletes, suggesting a relatively consistent CAR pattern across sports played at the elite level.