Goku’s first fight against Vegeta happened after the Saiyan Prince invaded Earth with the intention of decimating the planet and then selling what was left of it to the highest bidder, so naturally, Goku couldn’t let that happen. While Vegeta’s plans were foiled by the intervention of the Z-Fighters, Vegeta still effectively beat Goku personally by turning into a Great Ape and crushing Kakarot in his hands.

Vegeta proved that his mastery over his Saiyan power/transformation was greater than that of Goku, and Vegeta won as a result. In fact, this first fight established a trend that would carry on throughout most of their fights moving forward: Vegeta wins.

Goku Can’t Normally Beat Vegeta (Despite Seemingly Being Stronger)

Throughout every era of Akira Toriyama’s Dragon Ball series, Goku has consistently gotten increasingly stronger after every fight he’s in, and he is almost always the one who defeats the ultimate villain at the end of most sagas. More importantly, Goku always does so after Vegeta fails miserably first. Goku beat Frieza when Vegeta couldn’t, he assisted Gohan in eliminating Cell when Vegeta didn’t have a chance, and Goku delivered the Spirit Bomb during his final battle with Majin Buu while Vegeta sat powerless on the sidelines.

Not only that, but Goku has successfully attained almost every significant Saiyan transformation before Vegeta. Goku unlocked every new Super Saiyan transformation before Vegeta, and even channeled the power of the gods through Ultra Instinct before Vegeta finally figured out Ultra Ego. However, despite getting to the power-ups first and beating the villains Vegeta loses to, Goku can’t ever seem to get a clean victory when fighting Vegeta one-on-one.

The two times Goku has beaten Vegeta are when Vegeta wasn’t himself (literally). Baby Vegeta is a version of the Saiyan Prince from GT who was possessed by the Machine Mutant, Baby. This offered Vegeta a significant upgrade in terms of strength, but also limited his Saiyan potential (proven true when Baby Vegeta reached Golden Great Ape and didn’t go Super Saiyan 4). Goku beat Baby Vegeta, which is technically a victory, but one that could easily be contested. In a Dragon Ball Super anime-only story, Goku defeated ‘Duplicate Vegeta’, who was essentially a formless blob that turned into a version of Vegeta by siphoning his power. In every way that mattered, this was Vegeta, and Goku obliterated him with a Kamehameha Wave (though Duplicate Vegeta was accidentally weakened by Monaka first).

Both Dragon Ball GT and the anime-only stories of Dragon Ball Super have questionable canon status.

Out of the five fights they’ve been in, Goku has only beaten Vegeta twice, and those two victories weren’t even over the original Vegeta. Meanwhile, Vegeta has defeated Goku three out of the five times, even most recently in the much-debated training session on Beerus’ planet, which is their last recorded fight. Vegeta genuinely defeated the real Goku all three times. So, even though Goku is perhaps stronger than Vegeta when it comes to attaining transformations and defeating shared enemies, it is actually Vegeta who has won more of their Dragon Ball battles.