Partly as a result of poor commanders and partly because the Romans had
an innate and misguided belief in the invincibility of their legions,
the first battles against the Cimbri were a series of disasters. These
culminated in the Battle of Arausio in 105 BC when two Roman armies were
utterly destroyed.
Rome finally realized that their republic faced an existential threat,
and made the necessary painful political and military changes that were
needed to face that threat. Rome also found a commander who could take
on the Cimbri. Caius Marius was a deeply flawed man - scheming, cautious
to the point of cowardice, and quick to claim credit for the
achievements of others. Nevertheless, he was a massive improvement on
the leaders who had preceded him.
The reshaped Roman army eventually worked out how to weather the savage
onrush of the initial barbarian assault. Thereafter, the grim discipline
of the legions was enough to wear down the opposition. It helped that
Marius never fought unless the situation favored him, and as a result
his army gradually became accustomed to victory.
Had the Cimbri overwhelmed Rome, as at one time it seemed inevitable
that they would, then European history would have been very different.